03 - Rotational Motion Ex. 1 - 3 Module-2
LEVEL # 1
Questions
Conceptual Problems
Q.6 A particle, situated in an object, moves with
based on
Q.1 A wheel starts rotating from rest and attains an angular velocity of 60 rad/sec in 5 seconds. The total angular displacement in radians will be :
(A) 60 (B) 80
(C) 100 (D) 150
Q.2 A body rotates at 300 rotations per minute. The value in radian of the angle described in 1 sec is
(A) 5 (B) 5
(C) 10 (D) 10
Q.3 A chain couples and rotates two wheels in a bicycle. The radii of bigger and smaller wheels in a bicycle. The radii of bigger and smaller wheels are 0.5m and 0.1. respectively. The bigger wheel rotates at the rate of 200 rotations per minute, then the rate of rotation of smaller wheel will be -
(A) 1000 rpm (B) 50/3 rpm
(C) 200 rmp (D) 40 rpm
angular acceleration of 6 rad/sec2 and with
2 rad/sec angular velocity. If the radius of the circular path is 1m, its total acceleration in m/sec2 will be :
(A) 1 (B) 100
(C) 10 (D)
Q.7 A particle starts from rest under the effect of an angular acceleration of 5 rad/sec2. The value of angular displacement in 2 seconds in radian will be ?
(A) 10 (B) 20
(C) 20 (D) 50
Q.8 When a body rotates about an axis the quantity which remains same for all its particles, is
(A) linear velocity (B) angular velocity
(C) linear acceleration (D) angular momentum
Q.9 A wheel of an engine executes 4800 revolutions per minute. Its angular velocity (in rad/sec) would be
(A) 4800 (B) 2400
(C) 160 (D) 80
Q.10 A fan is rotating with a frequency 50Hz, its angular speed would be
Q.4 If the position vector of a particle is = (3 ‸i
‸
(A) 50 rad/sec (B) 200 rad/sec
100
+ 4 j ) metre and its angular velocity is
(C) 100 rad/sec (D) rad/sec
= ( ‸j + 2 k‸ ) rad/sec then its linear velocity is (in m/s)
(A) –(8 ‸i –6 ‸j + 3 k‸ ) (B) (3 i‸ + 6 ‸j + 8 k‸ ) (C) –(3 ‸i + 6 ‸j + 6 k‸ ) (D) (6 ‸i + 8 ‸j + 3 k‸ )
Q.5 A car is moving with a speed of 72 Km/hour.
Q.11 A particle moves by 1 cm in 1 sec in a path of radius 10cm. Its angular speed would be
(A) 10ΒΊ/sec (B) 10 rad/sec
(C) 0.1 rad/sec (D) 1 rad/sec
Q.12 Two particles of masses m1 and m2 complete one revolution of respective radii r1 and r2 in same time. The ratio of their angular speeds
would be -
The diameter of its wheels is 50cm. If its wheels come to rest after 20 rotations as a
(A) m
1r1
2 : m
2r22 (B) r1
: r2
result of application of brakes, then the angular retardation produced in the car will be
(A) 25.5 Radians/sec2
(B) 0.25 Radians/sec2
(C) 2.55 Radians/sec2
(D) 0
(C) r2 : r1 (D) 1 : 1
Q.13 When a mass rotates about any axis, the direction of the angular velocity will be :
(A) towards radius
(B) towards the tangent to the orbit
(C) at an angle of 45ΒΊ to the plane of rotation
(D) along the direction of axis of rotation
Q.14 If a rigid body a point rotates 60ΒΊ in 6 minutes the angular velocity of the body is
(A) 1/6 rad/sec (B) 3.14/18 rad/sec
(C) 3.14/180 × 6. (D) None of these
Q.15 A particle, moving along a circular path has equal magnitudes of linear and angular acceleration. The diameter of the path is (in metre) :
(A) 1 (B)
(C) 2 (D) 2
Q.21 The moment of inertia of a body does not depend on
(A) its mass
(B) angular velocity
(C) distribution of its particles
(D) its axis of rotation
Q.22 The moment of inertia of NaCl molecule with bond length r about an axis perpendicular to the bond and passing through the centre of mass is
Questions Moment of inertia
(A) (mNa
+ mCl
)r2 (B) mNa mCl r2
mNa xmCl
Q.16 The moment of inertia of a body depends
(C) mNa x mCl r2 (D) mNa mCl r2
upon -
mNa mCl
mNa mCl
(A) mass only
(B) angular velocity only
(C) distribution of particles only
(D) mass and distribution of mass about the axis
Q.17 On account of melting of ice at the north pole the moment of inertia of spinning earth -
(A) increases
(B) decreases
(C) remains unchanged
(D) depends on the time
Q.18 Two spheres of same mass and radius are in contact with each other. If the moment of inertia of a sphere about its diameter is I, then the moment of inertia of both the spheres about the tangent at their common point would be -
(A) 3I (B) 7I
(C) 4I (D) 5I
Q.19 Moment of inertia of a cylindrical shell of mass M, radius R and length L about its geometrical axis would be -
(A) MR2 (B) 1 MR2
2
Q.23 A disc of metal is melted to recast in the form of a solid sphere. The moment of inertia about a vertical axis passing through the centre would -
(A) decrease
(B) increase
(C) remains same
(D) nothing can be said
Q.24 Which of the following quantity is direction less
(A) moment of momentum
(B) Moment of force
(C) Moment of charge
(D) Moment of inertia
Q.25 The M.I. of a disc about its diameter is 2 units. Its M.I. about axis through a point on its rim and in the plane of the disc is
(A) 4 units. (B) 6 units
(C) 8 units (D) 10 units
Q.26 A solid sphere and a hollow sphere of the same mass have the same moments of inertia about their respective diameters, the ratio of their radii is
(A) (5)1/2 : (3)1/2 (B) (3)1/2 : (5)1/2
R2
L2
ML2
(C) 3 : 2 (D) 2 : 3
(C) M 4
12 (D) 12
Q.27 The physical significance of mass in
translational motion is same as that of the
Q.20 The moment of inertia of a sphere of radius R about an axis passing through its centre is proportional to -
(A) R2 (B) R3
(C) R4 (D) R5
following in rotational motion -
(A) moment of inertia
(B) angular momentum
(C) torque
(D) angular acceleration
Q.28 A stone of mass 4kg is whirled in a horizontal circle of radius 1m and makes 2 rev/sec. The moment of inertia of the stone about the axis of rotation is
(A) 64 kg × m2 (B) 4 kg × m2
(A) A > B
(B) A = B
(C) A < B
(D) depends on the actual values of t and r.
(C) 16 kg × m2 (D) 1 kg × m2
Q.29 In an arrangement four particles, each of mass
Questions
based on
Torque
2 gram are situated at the coordinate points (3, 2, 0), (1, –1, 0), (0, 0, 0) and (–1, 1, 0).
The moment of inertia of this arrangement about the Z-axis will be
(A) 8 units (B) 16 units
(C) 43 units (D) 34 units
Q.30 Two discs have same mass and thickness. Their materials are of densities 1 and 2. The ratio of their moment of inertia about
central axis will be -
(A) 1 : 2 (B) 12 : 1
(C) 1 : 12 (D) 2 : 1
Q.31 Three rings, each of mass P and radius Q are arranged as shown in the figure. The moment of inertia of the arrangement about YY’ axis will be
(A) 7 PQ2
2
2
Q.34 A disc of radius 2m and mass 200kg is acted upon by a torque 100N-m. Its angular acceleration would be
(A) 1 rad/sec2 (B) 0.25 rad/sec2
(C) 0.5 rad/sec2. (D) 2 rad/sec2.
Q.35 The product of moment of inertia and angular acceleration is -
(A) force
(B) torque
(C) angular momentum
(D) rotational kinetic energy
Q.36 The torque needed to produce an angular acceleration of 18rad/sec2 in a body of moment of inertia 2.5kg-m2 would be -
(A) 4.5 newton - metre
(B) 45 newton-metre
(C) 4.5 × 102 newton-metre
(D) 45 × 10–2 newton- metre
(B)
(C)
(D)
7 PQ2
2 PQ2
5
5 PQ2
2
Q.37 Dimensions of torque are -
(A) M2L2T–2 (B) M1L2T–2
(C) ML2T–1 (D) ML–1T2
Q.38 On applying a constant torque on a body -
(A) linear velocity increases
(B) angular velocity increases
Q.32 Three thin uniform rods each of mass M and length L and placed along the three axis of a Cartesian coordinate system with one end of each rod at the origin. The M.I. of the system about z-axis is
(C) it will rotate with constant angular velocity
(D) it will move with constant velocity
Q.39 A wheel starting with angular velocity of 10 radian/sec acquires angular velocity of 100 radian/sec in 15 seconds. If moment of inertia
is 10kg-m2, then applied torque (in newton-
(A)
ML2 3
ML2
(B)
2ML2
3
2
metre) is
(A) 900 (B) 100
(C) 90 (D) 60
(C)
(D) ML
6
Q.40 When a steady torque is acting on a body,
the body
Q.33 A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia IA and IB is
(A) continues in its state or uniform motion along a straight line
(B) gets linear acceleration
(C) gets angular acceleration
(D) rotates at a constant speed.
Q.41 A wheel of moment of inertia 5 x 10–3 kg-m2 is making 20rev/s. The torque required to stop it in 10 sec is -
(A) 2 × 10–2 N-m (B) 2 × 102 N-m (C) × 10–2 N-m (D) 4 × 10–2 N-m
Q.42 An automobile engine develops 100H.P. when rotating at a speed of 1800 rad/min. The torque it delivers is
(A) 3.33 W-s (B) 200W-s
(C) 248.7 W-s (D) 2487 W-s
Q.43 A disc of radius 1m and mass 1 kg is rotating with 40 radians/sec. the torque required to stop it in 10sec will be
(A) 1N-m (B) 2N-m
(C) 0.5N-m (D) 4N-m
Q.44 The moment of inertia and rotational kinetic energy of a fly wheel are 20kg-m2 and 1000
joule respectively. Its angular frequency per minute would be -
Q.48 A torque of 2 newton-m produces an angular acceleration of 2 rad/sec2 a body. If its radius of gyration is 2m, its mass will be :
(A) 2kg (B) 4 kg
(C) 1/2 kg (D) 1/4 kg
Q.49 The three similar torque () are acting at an angle of 120ΒΊ with each other. The resultant torque will be:
(A) zero (B)
(C) 3 (D) /3
Q.50 A ring of diameter 1m is rotating with an angular momentum of 10 Joules-sec. The necessary tangential force required to increase its angular momentum by 50% in 1sec will be (in newtons) :
(A) 10 (B) 5
(C) 15 (D) 20
Q.51 A particle is at a distance r from the axis of rotation. A given torque produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce
the same angular acceleration is
(A) 600
25
(B) 2
(C) 5
(D) 300
(A) /2 (B)
(C) 2 (D) 4
Q.45 A rigid body is rotating about a vertical axis at n rotations per minute, If the axis slowly becomes horizontal in t seconds and the body keeps on rotating at n rotations per minute then the torque acting on the body will be, if the moment of inertia of the body about axis of rotation is I.
2nI
(A) zero (B) 60t
4nI
Q.52 A body is rotating nonuniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is
(A) vertical
(B) horizontal and skew with the axis
(C) horizontal and intersecting the axis
(D) none of these
Q.53 Torque/moment of inertia equals to
(C) 60t
(D) 60t
(A) angular velocity
Q.46 A force of (2 ‸i – 4 ‸j + 2 k‸ ) Newton acts at a point (3 ‸i + 2 ‸j – 4 k‸ ) metre from the
origin. The magnitude of torque is
(A) zero (B) 24.4 N-m
(C) 0.244 N-m (D) 2.444 N-m
Q.47 The angular velocity of a body is
(B) angular acceleration.
(C) angular momentum.
(D) force
Q.54 Equivalent to force in rotational motion is
(A) moment of force (B) impulse
(C) moment of inertia (D) none of these
= 2 ‸i + 3 ‸j + 4 k‸
and a torque
Q.55 The radius of gyration of a rotating body
= ‸i + 2 ‸j + 3 k‸ power will be
acts on it. The rotational
depends upon -
(A) mass
(B) volume of the body
(A) 20 watt (B) 15 watt
(C) shape of the body
(C)
watt (D)
watt
(D) applied torque.
Questions Angular Momentum
Q.56 The rate of change of angular momentum is called
(A) angular velocity
(B) angular acceleration
(C) force
(D) torque
Q.57 A man sitting on a rotating stool with his arms stretched out, suddenly lowers his hands
(A) his angular velocity decreases
(B) his moment of inertia decreases.
(C) his angular velocity remains constant
(D) his angular momentum increases.
Q.58 The rotational kinetic energy of a rigid body
of moment of inertia 5 kg-m2 is 10 joules. The angular momentum about the axis of rotation would be -
(A) 100 joule-sec (B) 50 joule-sec
(C) 10 joule-sec (D) 2 joule -sec
Q.63 The torque applied to a ring revolving about its own axis so as to change its angular momentum by 2 J-s. in 5 s, is
(A) 10N-m (B) 2.5 N-m
(C) 0.1N-m (D) 0.4N-m
Q.64 The angular velocity of a body changes from one revolution per 9second to 1 revolution per second without applying any torque. The ratio of its radius of gyration in the two cases is
(A) 1 : 9 (B) 3 : 1
(C) 9 : 1 (D) 1 : 3
Q.65 A dog of mass m is walking on a pivoted disc of radius R and mass M in a circle of radius R/2 with an angular frequency n: the disc will revolve in opposite direction with frequency -
Q.59 A circular ring of mass 1kg and radius 0.2m executes 10 revolutions per sec. Its angular momentum would be - (kg-m2/sec)
(A) mn
M
2mn
(B) mn
2M
2Mn
(A) 0.025 (B) 0.25
(C) 2.5 (D) 25
(C)
M (D) M
Q.60 Which quantity is not directly related with rotational motion
(A) mass
(B) angular momentum
(C) torque
(D) moment of inertia
Questions Rotational Kinetic Energy
Q.66 The rotational kinetic energy is -
(A) m2 (B) 1 I2
2
(C) 1 I2 (D) 1 mv2
Q.61 A particle of mass m is rotating in a circular 2 2
path of radius r. Its angular momentum is J. The centripetal force acting on the particle would be -
Q.67 A circular ring of wire of mass M and radius R is making n revolutions/sec about an axis passing through a point on its rim and
(A)
J2
mr 2 (B)
J2r 2
J2
mr 3
perpendicular to its plane. The kinetic energy of rotation of the ring is given by-
(A) 42MR2n2 (B) 22MR2n2
(C)
m
(D) J2rm
(C)
1 2MR2n2 (D) 82MR2n2
Q.62 When a mass is rotating in a plane about a fixed point, its angular momentum is directed along-
(A) radius
(B) the tangent to the orbit
(C) a line perpendicular to the plane of rotation
(D) none of the above
2
Q.68 Rotational kinetic energy of a disc of constant moment of inertia is -
(A) directly proportional to angular velocity
(B) inversely proportional to angular velocity
(C) inversely proportional to square of angular velocity
(D) directly proportional to square of angular velocity
Q.69 The kinetic energy of a body rotating with constant angular velocity only depends upon its -
(A) mass
(B) radius of gyration
(C) moment of inertia
(D) angular momentum
Q.70 Rotational kinetic energy of a given body about an axis is proportional to -
(A) time period (B) (time period)2
Q.76 A disc rolls on a table. The ratio of its K.E. of rotation to the total K.E. is -
(A) 2/5 (B) 1/3
(C) 5/6 (D) 2/3
Q.77 A hoop having a mass of 1kg and a diameter of 1 meter rolls along a level road at 2m/sec. Its total K.E. would be -
(A) 1 Joule (B) 4 joules
(C) 2 joules (D) 0.5 joule
Q.78 A cylinder of mass M and radius R rolls on an inclined plane. The gain in kinetic energy is
(C) (time period)-1 (D) (time period)–2
(A)
1 Mv2 (B)
2
1 I2
2
Q.71 A circular disc has a mass of 1kg and radius
(C) 3 Mv2 (D) 3 I2
40 cm. It is rotating about an axis passing 4 4
through its centre and perpendicular to its
plane with a speed of 10rev/s. The work done in joules in stopping it would be-
(A) 4 (B) 47.5
(C) 79 (D) 158
Q.72 A fly wheel of moment of inertia I is rotating at n revolutions per sec. The work needed to double the frequency would be -
(A) 22In2 (B) 42In2
(C) 62In2 (D) 82In2
Q.73 A thin bar of length L is suspended from one end and rotated at a speed of n revolutions per second. The rotational kinetic energy of the bar is -
(A) 2ML22n2 (B) 1/2 ML22n2. (C) 2/3 ML22n2 (D) 1/6 ML22n2.
Questions Rolling Motion
Q.74 A ring of mass 1kg and diameter 1m is rolling on a plane road with a speed 2m/s. Its kinetic energy would be -
(A) 1 joule (B) 4 joule
Q.79 The condition that a rigid body is rolling without slipping on an inclined plane is
(A) it has acceleration less than g.
(B) it has rotational and translational K.E. to be equal
(C) it has linear velocity equal to radius times angular velocity
(D) the plane is fricitionless.
Q.80 A disk and a ring of the same mass are rolling to have the same kinetic energy. What is ratio of their velocities of centre of mass
(A) (4:3)1/2 (B) (3 : 4)1/2
(C) (2)1/2 : (3) 1/2 (D) (3)1/2 : (2)1/2
Q.81 A rolling body has the maximum fraction of rotational energy equal to -
(A) 1/2 (B) 1/3
(C) 2/3 (D) 2/7
Q.82 The acceleration down the plane of spherical body of mass m radius R and moment of inertia I having inclination to the horizontal is
(C) 2 joule (D) 0.5 joule
gsin
gsin
Q.75 A disc is rolling without slipping. The ratio of (A)
its rotational kinetic energy and translational 1 I2 / R2 (B) 1 I / R2
kinetic energy would be - gsin gsin
(A) 1 : 1 (B) 2 : 1 (C) 1 I / MR2 (D) MR2 I
(C) 1 : 2 (D) 1 : 4
Q.83 A ring takes time t1 in slipping down an inclined plane of length L, whereas it takes
time t2 in rolling down the same plane. The
Q.86 A sphere rolls down an inclined plane through a height h. Its velocity at the bottom would be
ratio of t1 and t2 is -
(A) (2)1/2 : 1 (B) 1 : (2)1/2
(C) 1 : 2 (D) 1 : 21/4
Q.84 A solid cylinder starts rolling from a height h on an inclined plane. At some instant t, the
(A)
(C)
(B)
(D) gh
ratio of its rotational K.E. and the total K.E. would be
(A) 1 : 2 (B) 1 : 3
(C) 2 : 3 (D) 1 : 1
Q.85 When different regular bodies roll down along
Q.87 If the applied torque is directly proportional
to the angular displacement , then the work done in rotating the body through an angle would be - (C is constant of proportionality)
(A) C (B) 1 C
2
an inclined plane from rest, then acceleration will be maximum for a body whose -
(A) radius of gyration is least
(C) 1 2
C2 (D) C
(B) mass is least
(C) surface area is maximum
(D) moment of inertia is maximum
Q.88 Rotational power in rotational motion is -
(A) . (B) x
(C) . (D) x
LEVEL # 2
Q.1 A string of negligible mass is wrapped on a cylindrical pulley of mass M and radius R. The other end of string is tied to a bucket of mass m. If the pulley rotates about a horizontal axis then the tension in the string is -
(A) mg (B) (M + m) g
(A) 10-1rad/s2 (B) 10-2rad/s2
(C) 10-3rad/s2 (D) 10-4rad/s2
Q.6 A thin rod of mass 3kg and length 3m is bent in the form of an equilateral triangle. The moment of inertia of the triangle about an axis passing through its centre of mass and
(C)
Mmg (M 2m)
(D)
2mg (M 2m)
perpendicular to its plane would be - (in kg-m2)
(A) 1/6 (B) 1/3
Q.2 In the above problem the linear acceleration of the bucket would be -
(A) mg/(M + m) (B) Mg/(M + m)
(C) 5/12 (D) 1/2
Q.7 A solid sphere is placed on a horizontal plane. A horizontal impulse I is applied at a distance
2Mg
(C) (M 2m)
2mg
(D) (M 2m)
h above the central line as shown in the figure. Soon after giving the impulse the
Q.3 A small ball of radius r rolls down without sliding in a big hemispherical bowl. of radius
R. What would be the ratio of the translational
sphere starts rolling. The ratio h
R
1
would be
and rotational kinetic energies at the bottom of the bowl
(A) 2 : 1 (B) 3 : 2
(C) 4 : 3 (D) 5 : 2
Q.4 A smooth uniform rod of length L and mass M has identical beads of negligible size, each of mass m , which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity 0 about an axis
perpendicular to the rod and passing through
the mid point of the rod., There are no external forces. When the beads reach the ends of the rod, the angular velocity of the rod would be -
(A) 2
I
(B) 2 5
(C) 1 4
(D) 1 5
Q.8 A wheel whose radius is R and moment of inertia about its-own axis is I, rotates freely about its own axis. A rope is wrapped on the wheel. A body of mass m is suspended from the free end of the rope. The body is released from rest. The velocity of the body after falling a distance h would be -
(A) M0
(B) M0
mgh1/ 2
2mgh 1/ 2
M 2m
M 4m
(A) I
(B)
m I
(C) M0
(D) M0
1/ 2
1/ 2
M 6m
M 8m
2mgh
m I
(C)
m I / r 2
(D)
2mgh
12N
Q.5 In the figure a = 6 cm and b = 20 cm. If the moment of inertia of the system
is 3200 kg-m2, its
angular acceleration would be -
10N
30ΒΊ(
b
7N
Q.9 In the following figure, a body of mass m is tied at one end of a light string and this string is wrapped around the solid cylinder of mass M and radius R. At the moment t = 0 the system starts moving. If the friction is negligible, angular velocity at time t would be
(A)
(B)
(C)
mgRt (M m)
2Mgt (M 2m)
2mgt R(M 2m)
2mgt
unstable system is released. When the object passes the position right below the centre the angular velocity of the system would be
(D)
R(M 2m)
m (A)
(B)
(C)
(D)
Q.10 A ring or radius 3a is fixed rigidly on a table. A small ring whose mass is m and radius a, rolls without slipping inside it as shown in the figure. The small ring is released from position A. When it reaches at the lowest point, the speed of the centre of the ring at that time would be -
(A)
(B)
Q.14 A disc of mass 25kg and diameter 0.4m is rotating about its axis at 240rev/min. The tangential force needed to stop it in 20 sec would be -
(A) (B) 2
(C) 0.25 (D) 0.5
Q.15 A solid sphere of mass m is situated on a horizontal surface and a tangential force acts at the top of the sphere. If the sphere rolls without slipping then the acceleration of the centre of the sphere would be -
(C)
(D)
(A) 5 3
F (B) 3F
m 5m
Q.11 Three rings each of mass M and radius R
(C)
10F (D)
7m
7F
10m
are arranged according to the figure. The moment of inertia of this system about an axis XX' on its plane would be
Q.16 A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in
(A)
7 MR2
2
9
(B) (B)
5 MR2
2
2
a horizontal plane about an axis passing through one of its ends with a uniform angular velocity . The force exerted by the liquid at the other end is -
(C) (C)
MR2 (D)
2
MR2
5
(A) M2L2
(B)
M 2L2
Q.12 A thin rod is hinged at one end O and it is in an unstable equilibrium position. It falls under gravity due to a slight disturbance. It
(C) M2
L (D)
2
M2L 2
makes angles 60ΒΊ, 90ΒΊ and 180ΒΊ with vertical in positions (B), (C) and (D) respectively. If
2 3,4 are angular velocities at these positions, then -
(A) 4=23
(B) 4 = 22
(C) 4 = 1.5 2
(D) 4 = 2
Q.17 A solid cylinder of mass m rests on two
horizontal planks. A thread is wound on the cylinder in such a way that one end of it is hanging. The free end of thread is pulled vertically down with a constant force
F. The linear acceleration of the
Q.13 A disc of mass M and radius R is suspended in a vertical plane by a horizontal axis passing through its centre. After sticking an object of
cylinder would be -
(A) F m
(B) 3 F
4 m
same mass M at its rim the mass is raised to the position of maximum height. Now this
(C)
2F (D) 2F
5m 3m
Q.18 A solid cylinder of mass 250gm and radius 4cm is rolling down an inclined plane. The angle of inclination of the plane with horizontal
(A) IA = IB (B) IA > IB
(C) IA < IB (D) IA > = < IB
Q.24 Two bodies with moments of inertia I1 and I2
–1 1
( I > I ) have equal angular momenta. If
is = sin 10 . Total kinetic energy of the 1 2
cylinder after 5 seconds would be-
(A) 0.02 joule (B) 0.2 joule
(C) 2.0 joules (D) 20 joules
Q.19 A wheel is rolling uniformly along a level road (see figure). The speed of transitional motion of the wheel axis is V. What are the speeds of the points A and B on the wheel rim relative to the road at the instant shown in the figure?
(A) VA = V ; VB = 0
(B) VA = 0; VB = V
(C) VA = 0 ; VB = 0
(D) VA = 0; VB = 2V
kinetic energy of rotation are E1 and E2
(A) E1 = E2 (B) E1 > E2
(C) E1 < E2 (D) E1 > = < E2
Q.25 Two discs have same mass and thickness.
Their materials are of densities 1 and 2 . The ratio of their moment of inertia about
central axis will be -
(A) 1 : 2 (B) 1 2 : 1
(C) 1 : 1 2 (D) 2 : 1
Q.26 A rigid body of mass m rotates with angular velocity about an axis at a distance a from the centre of mass G. The radius of gyration about a parallel axis through G is k. The kinetic energy of rotation of the body is
Q.20 A solid iron sphere A rolls down an inclined plane, while another hollow sphere B with the same mass and external radius also rolls
(A)
1 mk22 (B)
2
1 ma22
2
down the inclined plane. If VA and VB are
(C) 1 m (a2 + k2)2 (D) 1 m (a + k)2
their velocities at the bottom of the inclined 2 2
plane, then
(A) VA > VB (B) VA = VB
(C) VA < VB (D) VA > = < VB
Q.21 In question no. 44 if EA and EB be the total kinetic energies of A and B, then
Q.27 A metal sphere of radius R and specific heat s is rotating at a speed of n rotations per second about its central axis. It is suddenly stopped and 50% of its energy is converted into heat, the rise in temperature will be -
(A) EA > EB (B) EA = EB
2 2 2 2
4 R22n2
(C) EA < EB (D) EA > = < EB
(A)
5 JR
n s (B) 5 Js
Q.22 A person supports a book between finger and thumb as shown (the point of grip is assumed to be at the centre of the book). If the book
(C)
4 J2R22n2
5 s
(D)
2 R22n2
5 Js
has a weight of W then the person is producing a torque on the book of
a
Q.28 Two identical discs roll from rest on two inclined planes of length S and 2S as shown.
The velocities v1 and v2 acquired by the discs
(A) W 2 anticlockwise
(B) W b anticlockwise
2
at the bottom are related as -
(A) v1 = v2/4
(B) v1 = v2/2
(C) v1 = v2 1
(C) Wa anticlockwise
(D) Wa clockwise
Q23 Two circular discs A and B are
of equal
(D) v1 = 2v2
Q.29 A body of radius R and mass m is rolling on a horizontal plane without slipping with speed
masses and thickness but made of metals
with densities dA and dB (dA > dB). If their moments of inertia about an axis passing
through centres and normal to the circular faces be IA and IB , then
v. It then rolls up a hill of vertical height h. If h = 3v2/4g, the body is -
(A) Ring (B) Cylinder
(C) Solid sphere (D) Spherical shell
Q.30 From a disc of mass M and radius R, a concentric disc of radius r and mass m is removed. The remaining portion will have moment of inertia about its symmetric axis as -
Q.35 Three particles are connected by light, right rods lying along the y-axis. If the system rotates about the x-axis with an angular speed of 2rad/s, the
M m
(A) 2 (R – r)
M m
(C) 2 (R – r)
2 (B) M m (R2 – r2).
2 (D) M m (R2 + r2)
M.I. of the system is
(A) 46 kg-m2
(B) 92kg-m2
(C) 184 kg-m2
Q.31 Two particles of masses m1 and m2 are connected at the two ends of a weightless rod of length l. The rod is rotated about a perpendicular axis passing through the centre
of mass of the two particles at a speed of n revolutions per second. The rotational K.E. of the system is
(A) 42n2l2 x m1m2
1 2
(B) 22n2l2 x m1m2
1 2
(C) 42n2l2 x (m1 + m2)
(D) 22n2l2 x (m1 + m2)
Q.32 A uniform cylinder of mass m and radius R starts descending at a moment t = 0 due to gravity. Neglecting the mass of the thread, the tension of each thread is
(A) mg. (B) mg/2
(C) mg/3 (D) mg/6
Q.33 A thin rod of length l and mass m is suspended freely at its end. It is pulled aside and swung about a horizontal axis, passing
through its lowest position with an angular speed . Through what height centre of mass has been raised
(A) 2l2/g. (B) 2l2/6g
(C) 2l2/2g (D) 2l2/3g
Q.34 Two masses of 3kg and 5kg are placed at
(D) 276 kg-m2
Q.36 In the above problem, the total kinetic energy of the system is
(A) 92J (B) 184 J
(C) 276 J (D) 46 J
Q.37 A 12-kg mass is attached to a cord that is wrapped around a wheel of radius r = 10cm. The acceleration of the mass down the frictionless incline is measured to be 2.0m/s2.
The tension in the rope is -
(A) 23.4 N
(B) 70.2 N
(C) 93.6N
(D) 46.8N
Q.38 A uniform solid cylinder of mass M and radius R rotates on a horizontal, frictionless axel. Two masses hung from light cords wrapped around the cylinder. If the system is released from rest, the tension in each cord is
Mmg
20cm and 70cm marks respectively on a light wooden meter scale. The M.I. of the system about an axis passing through 100 cm mark and perpendicular to the meter scale is
(A) 2.17kg-m2 (B) 2.37 kg-m2
(C) 2.57 kg-m2 (D) 2.77 kg-m2
(A)
(B)
(C)
(D)
(M m)
Mmg (M 2m)
Mmg (m 3m)
Mmg (M 4m)
Q.39 In the above problem, acceleration of each mass is
Q.42 The moment of inertia of a cylindrical shell of external and internal radii R and r and mass
(A)
4mg M 4m
(B)
4mg M m
M about a vertical axis perpendicular to its length l is -
2mg
2mg
R2 r 2
Mπ2
(C)
M m
(D)
M 2m
(A) M
2 + 12
R2 r 2
Mπ2
Q.40 In problem 56, the angular velocity of the
cylinder after the masses have fallen a
(B) M
2 + 3
distance h is
π2 3R2 3r 2
(A) 1 R
(B) 1 R
(C) M
12
1 1 R2 r 2
Mπ2
(C) R
(D) R
(D) M
4 + 12
Q.41 In the figure a = 5cm and b = 20cm. If the
M.I. of the wheel is 3200kg-m2, the angular acceleration would be
(A) 10–1 rad/s2 (B) 10–2rad/s2
(C) 10–3 rad/s2 (D) 10–4 rad/s2
Q.43 A rod of mass 3 kg and of length 3m is bent in the form of an equilateral triangle. The moment of inertia of the triangle about a vertical axis perpendicular to plane and passing through centre of mass is
(A) 1/6kg m2 (B) 1/3 kg m2
(C) 5/12 kg m2 (D) 1/2 kg m2
LEVEL # 3
Q.1 A ring of mass m and radius R has three
8m
2m
particles attached to the ring as shown in the
figure. The centre of the ring has a speed v0. The kinetic energy of the system is : (Slipping
(A)
4m M
m
(B)
4m M
4m
is absent.)
(C) M m
(D)
2M m
Q.5 The distance of the centre of mass of T–shaped plate from O is –
(A) 6 mv02 (B) 12 mv 2
(C) 4 mv 2 (D) 8 mv 2
(A) 7m (B) 2.7m
(C) 4m (D) 1m
0 0
Q.2 A disc of radius r rolls on without slipping on a rough horizontal floor. If velocity of its centre of mass is v then velocity of point p, as shown in the figure (OP = r/2 and QOP = 60ΒΊ) is
Q.6 A solid uniform sphere rotating about its axis with kinetic energy E1 is gently placed on a rough horizontal plane at time t = 0. Assume that at time t = t1, it starts pure rolling and at that instant total K.E. of the sphere is E2. After sometime at time t = t2, K.E. of the sphere is E3. Then –
(A) E1 = E2 = E3 (B) E1 > E2 = E3 (C) E1 > E2 > E3 (D) E1 < E2 = E3
(A) v0
v0(C) 7
2
(B) v 0
2
v0(D) 3
2
Q.7 A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53ΒΊ with it. The other end rests on a rough horizontal floor. Find the normal force and the
Q.3 A particle of mass 2 kg located at positon
frictional force that the floor exerts on the ladder
(Λi Λj) m has a velocity 2 (Λi Λj kΛ) m/s. Its
angular momentum about z–axis in kg–m2/s is –
(A) zero (B) +8 (C) 12 (D) –8
Q.4 Two men each of mass m stand on the rim of a horizontal circular disc, diametrically opposite to each other. The disc has a mass M and is free to rotate about a vertical axis passing through its centre of mass. Each mass start simultaneously along the rim clockwise and reaches their original starting points on the disc. The angle turned through by the disc with respect to the ground (in radian) is –
(A) 65 N, 65 N, 98 N (B) 65 N, 98 N, 65 N
(C) 98 N, 65 N, 65 N (D) 65 N, 65 N, 65 N
Q.8 Two uniform rods of equal length but different masses are rigidly joined to form an L–shaped body, which is then pivoted as shown. If in equilibrium the body is in the shown configuration, ratio M/m will be –
(A) 2 (B) 3 (C)
(D)
from its unstable equilibrium position. When it has turned through an angle its average angular velocity is given as –
Q.9 A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the string and pulls the cylinder towards him (figure). There is no slipping anywhere. The length of the string
(A)
6g sin L
(B)
sin
2
passed through the hand of the man while the cylinder reaches his hands is –
(C)
6g cos (D) 6g cos
L 2 L
(A) l (B) 2l (C) 3l (D) 4l
Q.13 A sphere of mass M rolls without slipping on the inclined plane of inclination . What should be the minimum coefficient of friction, so that the sphere rolls down without slipping ?
Q.10 A uniform rod AB of length L and mass M is
2
(A) 5
tan (B) 2
7
tan
lying on a smooth table. A small particle of mass m strike the rod with a velocity v0 at point C a distance x from the centre O. The particle comes to rest after collision. The value of x, so that point A of the rod remains stationary just after collision, is –
(C) 5 tan (D) tan
7
Q.14 A cubical block of mass m and edge a slides down a rough inclinded plane of inclination with a uniform speed. Find the torque of the normal force acting on the block about its centre –
1
(A) mga sin (B) 3 mga sin
(C)
1 mga sin (D)
4
1 mga sin
2
(A) L/3 (B) L/6 (C) L/4 (D) L/12
Q.11 A sphere is rolled on a rough horizontal surface. It gradually slows down and stops.
The force of friction tries to
(A) decrease the linear velocity
(B) increase the angular velocity
(C) increase the linear momentum
(D) decrease the angular velocity
Q.12 A uniform rod of length L is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest
Q.15 A hollow straight tube of length l and mass m can turn freely about its centre on a smooth horizontal table. Another smooth uniform rod
of same length and mass is fitted into the tube so that their centres coincide. The system is set in motion with an initial angular velocity
0. The angular velocity of the rod at an instant
when the rod slips out of the tube is – (A) 0/3 (B) 0/2 (C) 0/4 (D) 0/7
Passage Based Questions -
A rod of mass M and length L is suspended by a frictionless hinge at the point O as shown in figure. A bullet of mass m moving with velocity v in a horizontal direction strikes the end of the rod and gets embedded in it.
Q.16 The angular momentum of the system, about O before collision is -
(A) mvL (B) MvL
Q.19 Statement-I: If the earth expands in size without any change in mas, the length of the day would increase.
Statement-II: The rotation of earth about its axis follows the law of conservation of angular momentum.
Q.20 Statement-I: A body moving in a straight line parallel to Y-axis can have angular momentum.
Statement-II: We can employ the concept of angular momentum only in rotatory motion
Q.21 Statement-I: When a planet is at maximum distance from the sun, its speed is minimum.
Statement-II: The motion of planet around the sun does not follow the law of conservation of angular momentum.
Q.22 Statement-I : When a sphere and a solid cylinder are allowed to roll down an inclined
(C)
1 mvL (D)
2
1 MvL
2
plane, the sphere will reach the ground first even if the mass and radius of the two bodies are different.
Q.17 When the bullet is embedded in the rod, the moment of inertia of the system about an axis passing through point O and perpendicular to the length of the rod is -
2
Statement-II : The acceleration of the body rolling down the inclined plane is directly proportional to the radius of the rolling body.
Q.23 Statement-I : Angular velocity is a
(A) (m + M)L2
L
(B) (m + M) 2
characteristic of the rigid body as a whole.
Statement-II : Angular velocity may be
(C) mL2 +
ML2 4
(D) mL2 +
ML2 3
different for different particles of a rigid body about the axis of rotation.
Q.18 The angular velocity by the rod just after the
collision is -
Q.24 Statement I : If bodies slide down an inclined
plane without rolling, then all the bodies reach
(A)
mv (3m M)L
2mv
(B) 2mv
ML
3mv
the bottom simultaneously.
Statement II : Acceleration of all bodies are
(C) L
(D)
(3m M)L
equal and independent of shape.
Q.25 Statement I : A wheel moving down a per-
Assertion & Reason Type Questions -
Each of the questions given below consist of Statement – I and Statement – II. Use the following Key to choose the appropriate answer.
(A) If both Statement- I and Statement- II are true, and Statement - II is the correct explanation of Statement– I.
(B) If both Statement - I and Statement - II are true but Statement - II is not the correct explanation of Statement – I.
(C) If Statement - I is true but Statement - II is false.
(D) If Statement - I is false but Statement - II is
fectly frictionless inclined plane shall undergo slipping (not rolling).
Statement II : For rolling torque is required, which is provided by tangential frictional force.
Q.26 Statement I : The centre of mass of a circular disc lies always at the centre of the disc. Statement II : Circular disc is a symmetrical body.
true.
Column Matching Type Questions -
Q.27 A particle of mass 1 kg is projected with velocity 20 2 m/s at 45ΒΊ with ground. When,
Q.29 A solid sphere is rotating about an axis as shown in figure. An insect follows the dotted path on the circumference of sphere as shown. Match the following:
the particle is at highest point: (g = 10 m/s2)
Column-I Column-II
(A) Net torque on the (P) 200 SI unit particle about point
of projection
(B) Angular momentum (Q) 400 SI unit of the particle about
point of projection
Column-I
Column-II
(C) Angular velcoity of (R) 1.0 SI unit particle about point of
projection
(S) None
Q.28 Match the following :
Column-I Column-II
(A) In pure rolling work (P) is always zero done by friction
(B) In forward slipping (Q) may be zero done by friction
(C) In backward slipping (R) is negative work done by friction(S)is positive
(T) may be negative
(U) may be positive
(A) Moment of inertia (P) will remain cons.
(B) Angular velocity (Q) will first increase
then decrease
(C) Angular momentum (R) will first decrease
then increase
(D) Rotational kinetic (S) will continuously energy decrease
(T) will continuously increase
(U) data is insufficient
LEVEL # 4
(Questions asked in previous AIEEE & IIT-JEE)
SECTION - A
Q.1 A ringof mass M andradius Rismoving inhorizontal plane at angular speedabout self axis. If twoequal point masses areplacedat theendsof any diameter. Find final angular speed of system -
(A) M (B) M
Q.6 A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness t/4. Then the relation between the moment of inertia IX and IY is
(A) IY = 16 IX (B) IY = IX
2m
(C) m
M 2m
M 2m
(D) none of above
(C) IY = 64 IX (D) IY = 32 IX
Q.7 A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is –
Q.2 The minimum velocity (in ms–1) with which a car driver must travels on a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is –
(A) 60 (B) 30
(C) 15 (D) 25
Q.3 A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)
(A) Solid sphere (B) Hollow-sphere
(C) Ring (D) All same
Q.4 Moment of inertia of a circular wire of mass M and raidus R about its diameter is –
(A) 2 L (B) 4 L
(C) L / 2 (D) L / 4
Q.8 A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected ?
(A) Moment of inertia
(B) Angular momentum
(C) Angular velocity
(D) Rotational kinetic energy
Q.9 One solid sphere A and another hollow sphere B are of same mass and same outer radi. Their moment of inertia about their diameters are respectively A and B such that –
(A) A = B (B) A > B
(A)
MR2
(B) MR2
(C) A
< B
(D) (D)
A = dA
B dB
2
(C) 2 MR2 (D)
MR2
where dA and dB are their densities.
Q.10 An annular ring with inner and outer radii R1
and
4
Q.5 In the following figure angular momentum of particle of mass m and speed v about origin is –
R2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on
F1
the inner and outer parts of the ring, F2 is
R R 2
(A) mvL
(C) mv/L
(B) mvπ
(D) mv/π
2
(A) R1
(C) 1 (D)
(B) 1
R2
R1 R2
Q.11 The moment of inertia of uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is
(A) F ( Λi Λj ) (B) – F ( Λi Λj )
(C) F ( Λi Λj ) (D) – F ( Λi Λj )
Q.15 Four point masses, each of value m, are placed
(A)
1 Mr 2
4
(B) 2 Mr 2
5
1
at the corners of a square ABCD of side π. The moment of inertia of this system about an axis passing through A and parallel to BD is –
(C) Mr2 (D)
Mr2
2
(A) 3 mπ2 (B) mπ2
Q.12 A 'T' shaped object with dimensions shown in
→
(C) 2 mπ2 (D) mπ2
the figure, is lying on a smooth floor. A force ' F ' is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.
Q.16 For the given uniform square lamina ABCD, whose centre is O,
F
D • C
•O
A • B E
2l (A)
IAC = IEF (B) IAD = 3IEF
(C) IAC = IEF (D) IAC =
IEF
(A)
2 π
3
4
(B) 3 π
2
Q.17 A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is R from the centre of the bigger disc. The value of is
(C) 3 π
(D) π
1 1 1 1
Q.13 A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity . Two objects each of mass M are attachecd gently to the opposite ends of a di- ameter of the ring. The ring now rotates with an angular velocity ' =
(A) 3 (B) 2 (C) 6 (D) 4
Q.18 A round uniform body of radius R, mass M and moment of inertia ‘I’, rolls down (without slipping) an inclined plane making an angle
m
(A) (m M)
m
(B) (m 2M)
with the horizontal. Then its acceleration
is
(m 2M)
(C) m
(m 2M)
(D) (m 2M)
(A)
gsin 1 I / MR 2
(B)
gsin 1 MR 2 / I
Q.14 A force of – F kΛ acts on O, the origin of the coordinate system. The torque about the point
(C)
gsin
1 I / MR 2 (D)
gsin
1 MR 2 / I
(1, – 1) is – z
y
x
Q.19 Angular momentum of the particle rotating with a central force is constant due to
(A) Constant Force
(B) Constant linear momentum
(C) Zero Torque
(D) Constant Torque
Q. 20 Consider a uniform square plate of side ‘a’
(C) = v
5a
(D) All of these
and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
Q.2 The moment of inertia of a thin square plate ABCD (figure) of uniform thickness about an axis passing through the centre O and perpendicular to the plane of the plate is
1 7
(A) 12 ma2 (B) 12 ma2
2 5
(C) 3 ma2 (D) 6 ma2]
Q.21 A thin uniform rod of length π and mass m is
(A) I1 + I2
(C) I1 + I3
(B) I3 + I4
(D) All of these
swinging freely about a horizontal axis passing through its end. Its maximum angular speed is
. Its centre of mass rises to a maximum height
of -
where I1, I2, I3 and I4 are respectively the moments of inertia about axes 1, 2, 3 and 4 which are in the plane of the plate.
Q.3 A symmetric lamina of mass M consists of
1
(A) 6
1
(C) 6
π
g
π22
g
1
(B) 2
1
(D) 3
SECTION - B
π22
g
π22
g
a square shape with a semicircular section over each of the edge of the square as shown in the figue. The side of the square is 2a. The moment of inertia of the lamina about an axis throught its centre of mass and perpen-
dicular to the plane is 1.6 Ma2. The moment
of inertia of the lamina about the tangent AB
Q.1 A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses m and 2m moving in the same hori- zontal plane with speed 2v and v respectively, strike the bar (as shown in the figure) and stick to the bar after collision. Denoting angu- lar velocity (about the centre of mass), total energy and centre of mass velocity by ;
E and V respectively, we have after collision–
2m
in plane of the lamina is ...............
(A) Vc = 0
3a
a 2a
(B) (B)
2v m
3mv2
5
(A) 4.8 Ma2 (B) 3.8 Ma2
(C) 2.8 Ma2 (D) 1.8 Ma2
Q.4 A uniform disc of mass m and radius R is rolling up a rough inclined plane which makes an angle of 300 with the horizonta. If the coefficient of static and kinetic friction are each equal to Β΅ and the only forces acting are gravitational and frictional, then the magnitude of the frictional force acting on the disc is ................ and its direction is
....................(write ‘up’ or ‘down’) the inclined
plane.
(A) mg/2, down (B) mg, down
(C) mg, up (D) mg/2, up
Q.5 Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. The moment of inertia of the plate about axis CD is then
(A)
(C)
L3
82
5L3
162
(B)
(D)
L3
162
3L3
82
equal to –
(A) I1 (B) I1 sin2
(C) I1 cos2 (D) I1 cos2(/2)
Q.6 A cubical block of side a is moving with ve- locity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is –
Q.9 An equilateral triangle ABC formed from a uniform wire has two small identical beads initially at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down are :
(A) 3v 4a
3 v
(C) 2a
(B) 3v 2a
(D) Zero
(A) angular velocity and total energy (kinetic and potential)
(B) total angular momentum and total energy
Q.7 A disc of mass M and radius R is rolling with angular speed w on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is :
(C) angular velocity and moment of inertia about the axis of rotation
(D) total angular momentum and moment of inertia about the axis of rotation.
(A)
(C)
1 MR2
2
3 MR2
2
(B) MR2
(D) 2MR2
Q.10 One quarter sector is cut from a uniform disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is –
Q.8 A thin wire of length L and uniform linear mass density is bent into a circular loop
(A) 1 MR2 (B) 1 MR2
with centre at O as shown. The moment of inertia of the loop about the axis XX´ is :
2 4
(C) 1 MR2 (D)
8
MR2
Q.11 A cylinder rolls up an inclined plane, reaches
some height, and then rolls down (without slipping throughout these motions). The di- rections of the frictional force acting on the cylinder are -
(A) up the incline while ascending and down the incline while descending
ticle is given an impulse MV as shown in the figure then angular velocity of the system would be :
(B) up the incline while ascending as well as descending
(C) down the incline while ascending and up the incline while descending
(D) down the incline while ascending as well
(A)
(C)
v
2π v
π
(B)
(D)
v
4π 2v
π
as descending
Q.12 A circular platform is free to rotate in a hori- zontal plane about a vertical axis passing through its centre. A tortoise is setting at the edge of the platform. Now, the platform is given an angular velocity 0. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform (t) will vary with time t as -
(A)
Q.15 A horizontal turntable is rotating with angular velocity ‘’ about a vertical axis passing through its center. A boy is sitting at the centre of the table. The moment of inertia of the system is I and the kinetic energy is K. The boy spreads his hand and the moment of inertia of the system becomes 2I. Then kinetic energy of system becomes
(A) K (B) 2K
(C) K/2 (D) K/4
Q.16 There are two points P & Q at equal distances from the centre of the disc C as shown in figure. If the disc is purely rolling, then relation between the magnitude of the velocities of the points is -
(A) VQ > VC > VP
(B) VQ < VP < VC
(B)
(C) VP
= Vc , V
2 P
= VQ
(D) VP < VC > VQ
(C) Q.17. A particle is moving on a circular path with decreasing velocity . Choose the correct option.
(D)
(A) angular momentum
(B) Only direction of →
→ is constant
vector is constant
Q.13 A particle is moving in horizontal uniform circular motion. The angular momentum of the particle is constant about the point :
(A) out side the circle
(B) on the circumfermce
(C) on the centre of circle
(D) inside the circle
(C) Acceleration is directed toward the centre
(D) Partical spirals towards centre
Q.18 Mass and radius of a circular disc is 9 M & R respectivley.Moment of inertia of the disc about an axis passing through point O after removal of a disc of Radius R/3 as shown in the figure is
Q.14 Two particles each of mass M are connected by a massless rod. The rod is lying on the smooth horizontal surface. If one of the par-
(A)
37 MR2 (B) 9 MR2
9
(C)
40 MR2 (D) 4MR2
9
reaches up to a maximum height of
3v2
4g
with
Q.19 Moment of inertia of solid sphere of mass m and radius R about axis passing through center of mass is as shown in figure 1. The sphere is moulded in the form of disc of radius 'r' and thickness 't'. The moment of inertia of disc about the axis shown in figure 2 is .
t
The radius of disc is
respect to the initial position. The object is
(A) ring (B) solid sphere
(C) hollow sphere (D) disc
Q.23 STATEMENT–1
If there is no external torque on a body about its centre of mass, then the velocity of the center of mass remains constant.
because STATEMENT –2
The linear momentum of an isolated system
(A)
(C)
(B)
(D)
remains constant.
(A) Statement–1 is True, Statement–2 is True; Statement–2 is a correct explanation for State- ment–1
Q.20 A ball is rolling on the track as shown in the figure. AB is rough surface and BC is smooth. Ball reaches to the height C. KA, KB and KC are the kinetic energies at A, B and C.
A
B
(A) hA > hC ; KB > KC (B) hA < hC ; KB > KC
(C) hA = hC ; KB = KC (D) hA > hC ; KA < KC
Q.21 A solid cylinder is rolling over an inclined plane as shown in the figure.
(A) friction force is dissipative
(B) on decreasing , frictional force decreases
(C) friction force does help in rotation and opposes translation
(D) friction force is necessarily Β΅mgcos
Q.22 A small object of uniform density rolls up a curved surface with an initial velocity v. It
(B) Statement–1 is True, Statement–2 is True; Statement–2 is NOT a correct explanation for Statement–1
(C) Statement–1 is True, Statement–2 is False
(D) Statement–1 is False, Statement–2 is True.
Q.24 STATEMENT – 1
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
and
STATEMENT – 2
By the principle of conservation of energy, the to- tal kinetic energies of both the cylinders are iden- tical when they reach the bottom of the incline.
Q.25 A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then –
→ → A →
(A)
VC VA 2(VB VC )
→ → → →
(B) VC VB VB VA
→ → → →
(C) | VC VA | 2 | VB VC |
→ → →
(D) | VC VA | 4 | VB |
ANSWER KEY LEVEL # 1
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. D D A A A C A B B C C D D C C D A B A D
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. B C A D D A A B D D A B C B B B B A D C
Q.No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. A D B D C B A D A A A B B A C D B C C A
Q.No. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
Ans. B C D B B C A D C D D C C B C B B C C A
Q.No. 81 82 83 84 85 86 87 88
Ans. A C B B A C C A
LEVEL # 2
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Ans. C D D C C B B C D A A B A A B D D C D A B B
Q.No. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Ans. C C D C D C B D B D B B B B D D A B C D D
LEVEL # 3
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. A C D A B B B D B B A,B B B C D A D D A C
Q.No. 21 22 23 24 25 26
Ans. C C C A A A
Column Matching 27 A Q B Q C S
28 A Q,T,U B Q,T,U C Q,T,U
29 A Q B R C P D R
LEVEL # 4
SECTION - A
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Ans. B B D B B C D B C D D C B D A C A A C C C
SECTION - B
Q .No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. D D A A A A C D B A B B C C C A B D A A ,D
Q .No. 21 22 23 24 25
Ans. B,C D D D B ,C
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