STAGE-1-TEST PAPER-1 (PHYSICS)
STAGE
SCREENING EXAMINATION
Directions : Select the most appropriate alternative A, B, C and D in questions 1-35.
1. A metallic shell has a point charge ' Q ' kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of force?
(A) (B)
(C) (D)
2. What is the maximum value of the force F such that the block shown in the arrangement, does not move?
(A) 20 N (B) 10 N
(C) 12 N (D) 15 N
3. Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends. What would be its angular velocity?
(A)
V (B) 2V
L L
V
(C) 3L
V
(D) 4L
4. A particle of mass m is taken through the gravitational field produced by a source S, from A to B, along the three different paths as shown in figure. If the work done along the paths , and is W, W and W respectively, then
(A) W = W = W (B) W > W= W
(C) W = W > W (D) W > W> W
5. The edge of a cube is a = 1.2 102 m. Then its volume will be recorded as : (A) 1.72 106 m3 (B) 1.728 106 m3
(C) 1.7 106 m3 (D) 1.73 106 m3
6. The temperature (T) versus time (t) graphs of two bodies X and Y with equal surface area are shown in the figure. If the emissivity and the absorptivity of X and Y are EX, EY and AX, AY respectively,
(A) EX > EY and AX > AY (B) EX < EY and AX > AY
(C) EX > EY and AX < AY (D) EX < EY and AX < AY
7. A 1m long metal wire of cross sectional area 10–6 m2 is fixed at one end from a rigid support and a weight W is hanging at its other end. The graph shows the observed extension of length ๐ of the wire as a function of W.
The Young’s modulus of material of the wire in S units is
(A) 5 104 (B) 2 105
(C) 2 1011 (D) 5 1011
8. In the adjacent diagram, CP represents a wavelength and AO and BP, the corresponding two rays. Find the condition on for constructive interference at P between the ray BP and reflected ray OP. (Given PR = d)
(A) cos = 3
2d
(B) cos =
4d
(C) sec – cos = d
4
(D) sec – cos = d
9. Two rods, one of aluminium and the other made of steel, having initial length ๐1and ๐2 are connected together
to form a single rod of length ๐ + ๐ . The coefficients of linear expansion for aluminium and steel are and
1 2 a s
respectively. If the length of each rod increases by the same amount when their temperature are raised by tยบC,
๐1
then find the ratio (๐1 ๐ 2 ) .
s
(A) a
s
a
(B) s
a
(C) (a s ) (D) (a s )
10. The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.
(A) 1.25 cm (B) 2.5 cm
(C) 1.05 cm (D) 2 cm
11. A ray of light (GH) is incident on the glass-water interface DC at an angle 'i'. It emerges in air along the water-air interface EF (see figure). If the refractive index of water ยตw is 4/3, the refractive index of glass ยตg is :
(A)
3
4 sin i
(B)
1
sin i
4 sin i
(C) 3
(D)
4
3 sin i
12. The electric potential between a proton and an electron is given by V =V0 ๐n
r
r0 , where r0 is a constant.
Assuming Bohr’s model to be applicable, write variation of rn with n, n being the principal quantum number?
(A) rn
n (B) r 1
n
(C) rn
n2 (D) r 1
n2
13. If the atom Fm257 follows the Bohr model and the radius of Fm257 is n times the Bohr radius, then find n. (A) 100 (B) 200
(C) 4 (D) 1/4
14. When an AC source of emf E = E0 sin (100 t) is connected across a circuit, the phase difference between the emf E and the current in the circuit is
observed to be 4 , as shown in the diagram. If the circuit consists possibly
only of R-C or R-L or L-C series, find the relationship between the two elements.
(A) R = 1k, C = 10 F (B) R = 1k, C = 1 F
(C) R = 1k, L = 10 H (D) R = 1k, L = 1H
15. For a positively charged particle moving in a x-y plane initially along the x-axis, there is a sudden change in its path due to the presence of electric and/or magnetic fields beyond P. The curved path is shown in the x-y plane and is found to be non-circular. Which one of the following combinations is possible.
(A)
→ → bหj ckห
→
(B) ห
→ ckห aหi
(C) → → cหj bkห
→
(D)
ห → ckห bหj
16. Which of the following circuit is correct verification of ohm's law.
(A) (B)
(C) (D)
17. An ideal gas under goes a cyclic process as shown in the given PT diagram, where the process AC is adiabatic. The process is also represented by :
(A) (B)
(C) (D)
18. A police car moving at 22 m/s, chases a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
(A) 33 m/s (B) 22 m/s
(C) zero (D) 11 m/s
19. For uranium nucleus how does its mass vary with volume?
(A) m V (B) m 1/V
(C) m (D) m V2
20. For a particle executing SHM the displacement x is given by x = A cos t. Identify the graph which represents the variation of potential energy (PE) as a function of time t and displacement x.
(A) I, III (B) II, IV
(C) II, III (D) I, IV
21. In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 m. When this length is changed to 0.35 m, the same tuning fork resonates with first overtone. Calculate the end correction.
(A) 0.012 m (B) 0.025 m
(C) 0.05 m (D) 0.024 m
22. A particle is in uniform circular motion in a horizontal plane. Its angular momentum is constant when the origin is taken at :
(A) centre of the circle (B) any point on the circumference of the circle
(C) any point inside the circle (D) any point outside the circle Y
23. A conducting loop carrying a current is placed in a uniform magnetic field pointing into B
the plane of the paper as shown. The loop will have a tendency to :
X
(A) contract (B) expand
(C) move towards +ve x-axis (D) move towards –ve x-axis
24. A current carrying loop is placed in a uniform magnetic field towards right in four different orientations,
V, arrange them in the decreasing order of Potential Energy -
(i) (ii)
(iii) (iv)
(A) , , V (B) , , , V
(C) , V, , (D) , V, ,
25. 2 kg ice at - 20 ยบC is mixed with 5 kg water at 20 ยบC . Then final amount of water in the mixture would be :
[ Given : specific heat of ice = 0.5 cal/g ยบC, specific heat of water = 1 cal/g ยบC, latent heat of fusion of ice = 80 cal/gm]
(A) 6 kg (B) 7 kg
(C) 3.5 kg (D) 5 kg
26. In the shown arrangement of the experiment of the meter bridge if the length AC corresponding to null deflection of galvanometer is x, what would be its value if the radius of the wire AB is doubled?
(A) x (B) x/4
(C) 4x (D) 2x
27. The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation :
(I) (II)
(III) (IV)
(A) IV < II < IV < I (B) II < III < IV < I
(C) I < IV < III < II (D) I < III < II < IV
28. A nucleus with mass number 220 initially at rest emits an -particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the -particle :
(A) 4.4 MeV (B) 5.4 MeV
(C) 5.6 MeV (D) 6.5 MeV
MAIN EXAMINATION
1. N-divisions on the main scale of a vernier callipers coincide with N + 1 divisions on the vernier scale. If each division on the main scale is of a units, determine the least count of the instrument.
2. Characteristic X-rays of frequency 4.2 × 1018 Hz are produced when transition from L shell to K shell take place in a certain target material. Use Mosley’s law to determine the atomic number of the target material. Given Rydberg constant R = 1.1 × 107 m–1.
3. In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter 5 cm is used. The air column in pipe resonates with a tuning fork of frequency 480 Hz when the minimum length of the air column is 16 cm (end correction for tube is 0.6 r). Find the speed of sound in air at room temperature.
4. An insulated box containing a monoatomic gas of molar mass M moving with a speed v0 is suddenly stopped. Find the increment in gas temperature as a result of stopping the box.
5. A soap bubble is being blown at the end of a very narrow tube of radius b. Air (density ) moves with a velocity v inside the tube and comes to rest inside the bubble. The surface tension of the soap solution is T. After some time the bubble, having grown to a radius r, separates from the tube. Find the value of r. Assume that r >> b so that you can consider the air to be falling normally on the bubble’s surface.
6. Show by diagram, how can we use a rheostat as the potential divider.
C
7. A radioactive element decays by emission. A detector records n beta particles in 2 seconds and in next 2 seconds it records 0.75n beta particles. Find mean life correct to nearest whole number.
[Given ln |2| = 0.6931, ln |3| = 1.0986.]
8. A particle of mass m, moving in a circular path of radius R with a constant speed v2 is located at point (2R, 0) at time t = 0 and a man starts moving with a velocity v1 along the positive y-axis from origin at time t = 0. Calculate the
linear momentum of the particle with respect to the man as a function of time.
9. A meniscus lens is made of a material of refractive index 2. Both its surfaces have radii of curvature R. It has two different media of refractive indices 1 and
3 respectively, on its two sides (shown in the figure). Calculate its focal length
for 1 < 2 < 3, when light is incident on it as shown
y
v1
(0,0) x
10. In a photoelectric effect experiment, photons of energy 5 eV are incident
on the photocathode of work function 3 eV. For photon intensity = 1015
W/m2 saturation current of 4.0 A is obtained. Sketch the variation of photocurrent ip against the anode voltage VA in the figure below for photon
intensity
(curve A) and
= 2 × 1015 W/m2 (curve B) (in JEE
graph was to be drawn in the answer sheet itself.)
11. Eight charges each of magnitude ‘ q ‘, are placed at the vertices of a cube of side a. The nearest neighbors of any charge have opposite sign.
Find the work required to dismantle the system.
R
12. There is a crater of depth 100
on the surface of the moon (radius R). A projectile is fired vertically upward from
the crater with a velocity, which is equal to the escape velocity v from the surface of the moon. Find the maximum height attained by the projectile.
13. A positive point charge q is fixed at origin. A dipole with a dipole moment → is placed along the x-axis far away
from the origin with → pointing along positive x-axis. Find : (a) the kinetic energy of the dipole when it reaches a distance d from the origin, and (b) the force experienced by the charge q at this moment.
14. Two infinitely long parallel wires carrying currents = 0 sin t and in opposite direction are placed a distance
3a apart. A square loop of side a of negligible resistance with a capacitor of capacitance C is placed in the plane of wires as shown in the figure . Find the maximum current in the square loop. Also sketch the graph showing the variation of charge on the upper plate of the capacitor as a function of time for one complete cycle taking
anticlokwise direction for the current in the loop as positive.
Q(t)
t
15. A ring of radius R having uniformly distributed charge Q is mounted on a light rod suspended by two identical strings. The tension in strings in equilibrium is T0. Now a vertical magnetic field is switched on and ring is rotated at constant angular velocity . Find the maximum with which the ring can be
rotated if the strings can withstand a maximum tension of 3T0 .
2
B
16. A liquid of density of 900 kg/m3 is filled in a cylindrical tank of upper radius
0.9 m and lower radius 0.3 m. A capillary tube of length ๐ is attached at the bottom of the tank as shown in the figure. The capillary has outer radius
0.002 m and inner radius a. When pressure P is applied at the top of the tank
volume flow rate of the liquid is 8 × 10–6 m3/s and if capillary tube is detached, H
the liquid comes out from the tank with a velocity 10 m/s. Determine the coefficient of viscosity of the liquid.
[Given :a2 = 10–6 m2 and a2 / ๐ = 2 × 10–6 m]
๐
17. A string of mass per unit length is tied at both ends such that one end of the string is at x = 0 and the other is at x = ๐. When string vibrates in fundamental mode amplitude of the mid point of the string is a, and tension in the string is T. Find the total oscillation energy stored in the string.
18. A prism of refracting angle 30ยบ is coated with a thin film of transparent material A
of refractive index 2.2 on face AC of the prism. A light of wavelength 6600 ร
is incident on face AB such that angle of incidence is 60ยบ, find
(a) the angle of emergence and (b) the minimum value of thickness of the
B C
coated film on the face AC for which the light emerging from the face
has maximum intensity.
[Given refractive index of the material of the prism is ]
19. Two point masses m1 and m2 are connected by a spring of natural length ๐0. The spring is compressed such that the two point masses touch each other and then they are fastened by a string. Then the system is moved with a velocity v0 along positive x-axis. When the system reaches the origin the string breaks (t = 0). The position of the point mass m1 is given by x1 = v0 t – A(1 – cos t) where A and are constants. Find the position of the second block as a function of time. Also find the relation between A and ๐0.
20. The top of an insulated cylindrical container is covered by a disc having emissivity 0.6 and conductivity
0.167 W/Km and thickness 1 cm. The temperature of the top of the lid is maintained at 127°C by circulating oil as shown : (a) Find the radiation loss to the surroundings in J/m2 s if temperature of surroundings is 27ยบC. (b) Also find the temperature of the circulating oil. Neglect the heat loss due to convection.
Given 17 108 Wm2K 4
3
ANSWER KEY TEST PAPER (PHYSICS) SCREENING EXAMINATION
1. (A) 2. (A) 3. (C) 4. (A) 5. (C)
6. (D) 7. (C) 8. (B) 9. (C) 10. (A)
11. (B) 12. (A) 13. (D) 14. (A) 15. (B)
16. (D) 17. BONUS 18. (B) 19. (A) 20. (A)
21. (B) 22. (A) 23. (B) 24. (A) 25. (A)
26. (A) 27. (A) 28. (B)
MAIN EXAMINATION
1. a
N 1
2. Z = 42 3. 336 m/s 4.
Mv2
0 5.
3R
4T
v 2
6. The rheostat is as shown in figure. Battery should be connected between A and B and the load between C and B.
7. 6.947 sec.
8. m v
sin v 2
ห v
cos v2 t v
หj 9.
f 3R
2
t i 2
R R
1
3 1
10. 11.
4kq2 3
12. h = 99.5 R
3
a
qp → →
pq ห 2
13. (a)
4
0d2
(b) F qE 2 3 i
14.
imax
0ac0 ln(2) .
15.
DT0
16. =
1 N - S/m2
17.
2a2T
max BQR2 ,
720
4๐
18. (a) 0ยบ , (b) 1500 ร
19. x2 = v2t +
m1 m1
m A (1 – cos t), ๐0 = m
1 A
2 2
20. (a) 595 watt/m2 (b) 162.6ยบC
STAGE
SOLUTIONS TEST PAPER (PHYSICS)
SCREENING EXAMINATION
1. Electric field is zero everywhere inside a metal (conductor). i.e., field does not exists inside a conductor and these are perpendicular to a metal surface (equipotential surface).
2. Free body diagram (F.B.D.) of the block (shown by a dot) is shown in figure.
For vertical equilibrium of the block,
N = mg + F sin 60ยบ =
3 g + 3 F
2
...(i)
f F cos 60ยบ or ยตN F cos 60ยบ
1 3F F
or
or g F
or F 2g or 20 N
Therefore, maximum value of F is 20 N.
3. Let ‘’ be the angular velocity of the rod. Applying,
Angular impulse = Change in angular momentum about centre of mass of the system
J · L =
M M
2 C
L
ML2 V
J=MV
(MV) = (2) · =
2 L
4. Gravitational field is a conservative force field. In a conservative force field, the work done is path independent.
W = W = W
5. V = ๐3 = (1.2 × 10–2 m)3 = 1.728 × 10–6 m–3
length (๐) has two significant figure, the volume (V) will also have two significance figures. Therefore, the correct answer is
dT
V = 1.7 × 10-6 m3
6. Rate of cooling
dt emissivity (E)
dT dT
From the graph,
dt x
dt y
E < E
Further emissivity (E) absorptive power (A) (good absorbers are also good emitters)
A < A
Hence the correct answer is (C).
Note : Emissivity is a pure ratio (dimensionless) while the emissive power has unit J/s or watt
๐ W
7. ๐ = YA
i.e. graph is straight line passing through origin (as shown in diagram ), the slope of which is
๐ .
YA
๐
๐ 1
1.0
(80 20)
Slope = YA
Y = A
slope
= 106
(4 1) 104
= 2.0 × 1011 N/m2
8. PR = d
PO = d sec
and CO = PO cos 2 = d sec cos 2
Phase difference between the two rays OP and BP is =
(one is reflected, while another is direct) Therefore condition for constructive interference should be
x =
, 3
.....
2 2
or d sec (1 + cos 2) = 2
d
or cos (2 cos2 ) =
2
or cos =
4d
9. Given ๐ = ๐
or ๐ t = ๐ t
๐1 s
1 a 2 s
๐ 2 a
๐1
๐1 ๐ 2
s
a s
10. Image formed by convex lens at
1 1 1
will act as a virtual object for concave lens. For concave lens
5cm
u f
1 1 1
or 4
20
or v = 5 cm Magnification for concave lens
26cm
4cm
m = v 5 1.25
u 4
As size of the image at is 2 cm. Therefore, size of image of will be 2 × 1.25 = 2.5 cm.
11. Applying
Snell’s law ( sin i = constant) at 1 and 2 we have
ยต sin i =
sin r
Air
90ยบ 2
and
sin r = (1) (sin 90ยบ)
or
1
= sin i
r eV0
12. U = eV = eV0 ๐n r
| F | r
0
This force will provide the necessary centripetal force. Hence
m2 eV0
or ...(i)
r r
mr = nh
...(ii)
Dividing equation (ii) by (i) we have
nh
mr = 2
or r n
13. r
2
=
(0.53 ร
) = (n × 0.53)ร
m n
m z z
m = 5 for Fm257 (the outermost shell) and z = 100
(5)2 1
n = 100 = 4
14. As the current leads the emf E by 4 , it is an R-C circuit.
tan =
XC or tan
R
1
4 = CR
CR = 1 As = 100 rad/s
1
The product of CR should be 100 s–1
correct answer is (a).
15. Electric field can deviate the path of the particle in the shown direction only when it is along negative y- direction. In the given options E is either zero or along x-direction. Hence it is the magnetic field which is really responsible for its curved path. Options (a) and (c) can’t be accepted as the path will be helix in that case (when
the velocity vector makes an angle other than 0ยบ, 180ยบ or 90ยบ with the magnetic field, path is a helix) option (d)
is wrong because in that case component of net force on the particle also comes in kห direction which is not acceptable as the particle is moving in x - y plane. Only in option (b) the particle can move in x-y plane.
In option (d) :
→ = → → →
Fnet
qE q(v B)
Initial velocity is along x-direction. So let → หi
→ = ห
ห ห ห
Fnet
q[ ai (vi (ck ai)]
In option (b)
→ = qa ห – qvc หj
Fnet i
16. Ammeter is always connected in series and voltmeter in parallel.
17. Out of the alternatives provided, none appears completely correct.
AB is an isothermal process (T = constant, P
decreasing and V increasing.
1 ). So P - V graph should be rectangular hyperbola with P
V
BC is an isobaric process. (P = constant V T). Temperature is increasing. Hence volume should also increase.
CA is an adiabatic process (PV = constant) Pressure is increasing. So volume should decrease. At point A, on isotherm AB and an adiabatic curve AC are meeting. We know that (slope of an adiabatic graph in P-V diagram)
= (slope of an isothermal graph in the same diagram) with > 1 or (Slope) adiabatic > (slope) isothermal. None of the given diagram fulfill all the above requirements.
18. The motorcyclist observes no beats. So the apparent frequency observed by him from the two sources must be equal.
f1 = Frequency recorded by motorcyclist from police car.
f2 = Frequency recorded by motorcyclist from stationary siren. For no beats f = f
330 v 165 330 v
176 330 22 330
Solving this equation we get, v = 22 m/s
19. Nuclear density is constant hence, mass volume or m V
20. Potential energy is minimum (in this case zero) at mean position (x = 0) and maximum at extreme positions (x = ± A)
At time t = 0, x = A. Hence P.E. should be maximum. Therefore graph is correct. Further in graph III, P.E. is minimum at x = 0. Hence this is also correct.
21. Let ๐ be the end correction. Given that,
Fundamental tone for a length 0.1 m = first overtone for the length 0.35 m.
4(0.1 ๐) =
2
4(0.35 ๐)
Solving this equation we get
๐ = 0.025 m = 2.5 cm
22. In uniform circular motion the only force acting on the particle is centripetal (towards center). Torque of this force about the center is zero. Hence angular momentum about center remain conserved.
23. Net force on a current carrying loop in uniform magnetic field is zero. Hence the loop can’t translate. So, options (c) and (d) are wrong. From Flaming’s left hand rule we can see that if magnetic field is perpendicular to paper inwards and current in the loop
is clockwise (as shown) the magnetic force Fm on each element of the loop is radially outwards, or the loops will have a tendency to expand.
24. U = MB = – MB cos
Here M = magnetic moment of the loop
= angle between M and B
U is maximum when = 180ยบ and minimum when = 0ยบ. So as decrease from 180ยบ to 0ยบ its P.E. also decreases.
25. Heat released by 5 kg of water when its temperature falls from 20ยบC to 0ยบC is,
Q = mc = (5) (103) (20 – 0) = 105 cal
when 2 kg ice at –20ยบC comes to a temperature of 0ยบC, it takes an energy
Q = mc = (2) (500) (20) = 0.2 × 105 cal
The remaining heat Q = Q – Q = 0.8 × 105 cal will melt a mass m of the ice, where
0.8 105
m = 80 103
= 1 kg
So, the temperature of the mixture will be 0ยบC,
mass of water in it is 5 + 1 = 6 kg and mass of ice is 2 – 1 = 1 kg.
AC
26. The ratio CB
27. P = i2R
will remain unchanged.
current is same, so P R
2 r 3r
In the first case it is 3r, in second case it is 3 r, in third case it is 3
RIII < RII < RIV < RI
III II IV I
28. Given that K1 + K2 = 5.5 MeV (i)
and in fourth case the net resistance is 2 .
K1
2
216m 4m
From conservation of linear momentum
P1 = P2
or
as P =
K2 = 54 K1 (ii)
Solving equations (i) and (ii) we get K = K.E. of -particle = 5.4 MeV.
MAIN EXAMINATION
1. (N + 1) divisions on the vernier scale = N divisions on main scale
1 division on vernier scale =
N
N 1
divisions on main scale
Each division on the main scale is of a units.
N
1 division on vernier scale = N 1 a units = a’ (say)
Least count = 1 main scale division – 1 vernier scale division
N a
= a – a’ = a – N 1 a =
N 1
1 1
2. E = h = Rhc (z – b)2 n2 n2
1 2
For K-series b = 1
= Rc (z – 1)2 n2
n2
Substituting the values
1 1
4.2 × 1018 = (1.1× 107) (3 × 108) (z – 1)2
1 4
(z – 1)2 = 1697
or z – 1 41 or z = 42
v
3. Fundamental frequency, f = 4(๐ 0.6r)
speed of sound v = 4f (๐ + 0.6r)
or v = (4) (480) [(0.16) + (0.6)(0.025)] = 336 m/s
4. Decrease in kinetic energy = increase in internal energy of the gas
0.6r
1 2 m 3 R
mv0 = nCv T = M 2 T
2
Mv2
T = 0
3R
5. The bubble will separate from the tube when thrust force due to striking air at B is equal to the force due to excess pressure
4T
Av2 = A
r
(A = area of bubble at B where air strikes)
6. The rheostat is as shown in figure. Battery should be connected C
between A and B and the load between C and B.
4T
r = 2
7. Let n0 be the number of radioactive nuclei at time t = 0. Number of nuclei decayed in time t are given n (1 – e–2), which is also equal to the number of beta particles emitted in the same interval of time. For the given condition,
n = n (1 – e–2) (i)
(n + 0.75 n) = n (1– e–4 ) (ii)
Dividing (ii) by (i) we get
1 e4
1.75 =
1 e
2
3
or 1.75 – 1.75 e–2 = 1 – e–4
1.75 e–2 –e–4 = 4
.....(iii)
Let us take e–2 = x
Then the above equation is, x2 – 1.75x + 0.75 = 0
1.75 (1.75)2 (4)(0.75) 3
or x =
2
or x = 1 and 4
3
From equation (iii) either e–2 = 1 or e–2 = 4
but e–2 = 1 is not accepted because which means = 0. Hence
3
e–2 = 4
or –2 In (e) = ln(3) - ln (4) = ln(3) – 2 ln(2) = ln(2) -
1 In(3)
2
Substituting the given values, = 0.6931 –
1 × (1.0986) = 0.14395 s–1
2
Mean life tmeans =
1 = 6.947 sec
8. Angular speed of particle about centre of the circle,
v2
= R , = t =
v2
R t
→ = (– v
sin หi + v2
cos หj )
v
v 2 = v2 sin R
t หi v2 cos R
t j
and → = v ห
linear momentum of particle w.r.t. man as a function of time is
9. For refraction at first surface, ยต1 < ยต2 < ยต3
2 1
v1
2 1
R
......(i)
For refraction at 2nd surface,
3 2
3 2
=
.....(ii)
v2 v1 R
Adding equations (i) and (ii) we get
3 3 1
v = R
or v2 =
3R
2 3 1
3R
Therefore, focal length of the lens would be
3
1
Ans.
10. Maximum kinetic energy of the photoelectrons would be
Kmax = E – W = (5 – 3) eV = 2eV
Therefore, the stopping potential is 2 Volt. Saturation current depends on the intensity of light incident. When the intensity is doubled the saturation current will also
become two fold. The corresponding graphs are shown in figure.
11. For potential energy of the system of charges, total number of charge pairs will be 8C or 28. Of these 28 pairs 12 unlike charges are at a separation ‘a’, 12 likes charges are at separation
a and
4 unlike charges are at separation 3 a . Therefore the potential energy of the system
1 (12)(q)(q)
(12)(q)(q)
(4)(q)(q)
1 q2
U
= –5.824
40 a
40
The binding energy of this system is therefore
1 q2
|U| = 5.824 .
So, work done by external forces in disassembling, this system of charges is
1 q2
W = 5.824
Ans.
12. Speed of particle at A, vA = escape velocity on the surface of earth
=
At highest point B, vB = 0
Applying conservation of mechanical energy, decrease in kinetic energy = increase in gravitational potential energy.
1 mv 2 U U
2 A B
GMm
A
GMm
GMm
R 2
1.5R2 0.5R
R R h 3
100
1 1 3 1 99 2 1
or
R R h 2R 2 100 R
Solving this equation we get h = 99.5 R Ans.
13. (a) Applying energy conservation principle,
increase in kinetic energy of the dipole = decrease in electrostatic potential energy of the dipole.
kinetic energy of dipole at distance d from origin
= U i – U f
→ → ห 1
q ห qp
or K.E. = 0 – (p E) p E
= (p i ) 4
i
d2 4 d2
Ans.
0 0
(b) Electric field at origin due to the dipole.
→ 1 2p ห →
E
40
d3 i
(Eaxis p)
→ → pq ห
Force on charge q.
F qE i
2 0 3
Ans.
14. For an element strip of thickness dx at a distance x from left wire, net magnetic field (due to both wires)
0
B = 2
0I
I
x +
1
0 I
2 3a - x (out wards)
1
= 2 x
3a x
Magnetic flux in this strip,
0I 1 1
d = BdS = 2 x
3a x a dx
2a
total flux = a d
0Ia
2a 1 1
0Ia
= 2
a x
3a x
dx or =
In (2)
= 0a In(2)
( I0
sin t ) (i)
Magnitude of induced emf,
- d dt
0aI0 In2
=
cos t = e
cos t
where e0 =
0aI0 In2
Charged stored in the capacitor,
q = Ce = Ce0 cos t (ii)
and current in the loop
dq
i = dt
= C e
sin t (iii)
0aI02C In2
imax = C e =
Ans.
Magnetic flux passing through the square loop
sin t [ From equation (i) ]
i.e., magnetic field passing through the loop is increasing at t = 0. Hence, the included current will produce
magnetic field (from Lenz’s law). Or the current in the circuit at t = 0 will be clockwise (or negative as per the given convention). Therefore, charge on upper plate could be written as,
q q0
t
- q0
q = + q cos t [ from equation (ii) ]
0aCI0 In2
Here q 0 = Ce0 =
The corresponding q – t graph is shown in figures.
15. Let m = mass of ring In equilibrium,
2 T0 = mg
mg
or T0 = 2
Magnetic moment, M = iA = 2 Q ( R 2 )
BQR2
= MB sin 900 =
2
Let T1 and T2 be the tension in the two strings when magnetic field is switched on. (T1 > T2) For translational equilibrium of ring is vertical direction,
T1 + T 2 = mg (ii)
For rotational equilibrium,
D
( T1 – T 2 ) 2
= =
BQR2
2
or T1 – T 2 =
Solving equations (ii) and (iii) we have
mg
BQR2
2D
BQR2
...........(iii)
T 1 = 2 + 2D
As T1
> T2
and maximum values of T1
can be 3T0 , we have
2
3T0
maxBQR2
mg T
2 = T0 + 2D
0
2
max =
16. When the tube is not there,
DT0
BQR2
Ans.
P + P
+ 1 + gH =
0 2
1
1 2 + P
2 2 0
P + gH = ( 2 – 2 )
2 2
A = A or =
1
A 2 2
1 1 2 2 1 A1
2
(0.3)2 2
1 22 A 2
1-
2
P + gh = 2
= × × 2
2
(0.9)
1 1
4 103
4 103 900
= × × (10)2 1- 81 = =
2
81 81
4
= 9 × 10 5 N / m2
This is also the excess pressure P.
By Poiseuille’s equation, the rate of flow of liquid in the capillary tube
(P)a4
Q = 8๐
(a2 )(P)
a2
(a2
2
)(P)
– 6
๐
8 × 10 = 8
๐
=
8 8 106
Substituting the values we have
-6 4 5 6
(10
=
) 10
9
(2 10 )
= 1 N - S/m2
720
Ans.
8 8 10 6
17. ๐ = 2
2
or = 2๐ , k =
= ๐
The amplitude at a distance x from x = 0 is given by
A = a sin kx
Total mechanical energy at x of length dx is
1
dE =
(dm) A2 2
2
= 1 (dx) (a sin kx)2 ( 2f )2
2
or dE = 2 m f 2 a2 sin2 kx dx (i)
2
Here f2 = 2 =
T
(4๐2 )
and k = ๐
Substituting these values in equation (i) and integrating it from x = 0 to x = l, we get total energy of string,
18. (a) sin i1 = sin r1 or sin 60 0 =
1
E =
sin r1
2a2T 4๐
Ans.
A
sin r = 2
300
600 300 900
or r1 = 30
0
Now r1 + r2 = A
r = A – r = 300 – 300 = 00 B C
Therefore, ray of light falls normally on the face AC and angle of emergence i = 00 .
(b) Multiple reflection occurs between surfaces of film. Intensity will be maximum if interference takes place in the transmitted wave.
For maximum thickness
x = 2t = ( t = thickness )
t =
6600
= 2 2.2
= 1500 ร
Ans.
19. (i) X1 = v0 t – A (1– cost)
m1x1 m2 x2
Xcm =
m2 m2
= v0 t
m1
X = v t + m2
A (1–cos t) Ans.
(ii) a1
d2 x1
= dt2
= – 2 A cos t
The separation X2
– X1
between the two blocks will be equal to ๐0
when a1
= 0 or cos t = 0
x2 – x1 =
m1 A (1–cos t) + A (1– cos t)
m2
๐0 =
m1 m
1 A (cos t = 0)
2
Thus the relation between ๐0 and A is,
๐0 =
m1
m2
1 A Ans.
20. (a) Rate of heat loss per unit area due to radiation
E = e (T4 – T4 )
Here T = 127 + 273 = 400 K
and T0 = 27 + 273 = 300 K
17
E = 0.6 × 3
× 10 - 8 [(400)2 – (300)2 ]
= 595 watt/m2 Ans.
(b) Let be the temperature of the oil.Then
rate of heat flow through conduction = rate of heat loss due to radiation
temperature difference thermal resistance
= (595) A
( - 127)
I
= (595) A
kA
Here A = area of disc ; k = thermal conductivity and l = thickness (or length) of disc
( – 127) k
l
= 595 = 595 k + 127
l
595 10 2
= 0.167
+ 127 z= 162.6 0C Ans.
STAGE
SIMILAR TEST PAPER (PHYSICS)
SCREENING EXAMINATION
1. A metallic shell has a charge q distributed over its surface and a large uncharged conducting plate is placed to the right side of the shell. Which diagram represents the electric lines of force correctly ?
(A) (B)
(C) (D)
2. Determine the magnitude of the force required such that the block moves with uniform motion on a rough fixed horizontal surface as shown -
(A) 10 N (B) 20 N
(C) 30 N (D) 15 N
3. Consider a uniform rod of mass M and length L and an impulse J imparted to it at the position 'P' shown. What would be its angular velocity?
(A) V 2L
V
(B) 3L
(C) 2V
L
(D) 3V
L
4. A particle of mass m is taken through the gravitational field produced by a point source S through two different paths and from point P to Q. If the workdone along the paths and are W and W respectively then choose the correct option if the source is not equidistant from points P and Q.
(A) W = W 0 (B) W = W = 0
(C) W > W (D) W < W
5. The radius of a circle is 2.12 × 10–2 m. The area enclosed by the circle is. (A) 1.41 × 10–3 m2 (B) 1.4 × 10–3 m2
(C) 1.4 × 10–2 m2 (D) 14.1 × 10–4 m2
6. The temperature (T) versus time (t) graph for two bodies X, Y with equal surface area is given. If the emissivity and the absorptivity of x and y are Ex,
Ey and ax, ay respectively. Then
(A) Ex > Ey , ax > ay (B) Ex > Ey , ax< ay
(C) Ex < Ey , ax = ay (D) Ex > Ey , ax = ay = 0
7. The percentage strain versus load curve is given for a wire of cross-sectional area 10–8 m2. The wire is fixed at one end from a rigid support and a weight W is hanging from its other end. Find the Young’s modulus of the wire
(A) 5 × 1014 N/m2 (B) 2 × 1014 N/m2
(C) 50 × 1012 N/m2 (D) 4 × 1014 N/m2
8. In the diagram EC and FB are the two rays parallel to the mirror principal axis. Find the condition on for which constructive interference at point B occurs between the ray ECB and incident ray FB, given AB = d?
(A) 2 sin–1 2d
(B) cos–1 d
(C) 2tan–1 2d
(D) 2 cot–1 2d
9. Three rods of aluminium, copper and steel have coefficient of linear expansion , , .When their temperature is raised by t°C the length of each rod increases by the same amount. Then L1 + L2 + L3 is proportional to -
(A) + + (B)
123
1 2 3
(C)
12 23 31
123
(D)
1 2 3
123
10. A concave lens of focal length 20cm forms the image of an object which is placed at infinity. The size of image formed is 1cm. If a convex lens of focal
length 10cm is placed 10cm from the concave lens. Find the new image size?
(A) 1.5 cm (B) 0.5 cm
(C) 2 cm (D) 1.2 cm
11. A ray of light is travelling in crown glass slab of refractive index . A
hemisphere made of flint glass having refractive index is placed on the
crown glass slab.The ray undergoes ref raction at BOD interface of the crown and f l int glass and above the hemispherical curve BCD a
medium of refractive index is present.
1
Determine ratio 3
if total internal reflection occurs at point C?
(A) (B)
(C) 3 2
(D)
e
12. The electric potential between a proton and an electron is given as U = – r 3 , where e is a constant. If the
Bohr's atomic model is applicable then the Bohr's radius (rn) and principal quantum number n are related as -
(A) rn
1 (B) r n
n n
1
(C) rn n2
(D) rn
n2
13. According to the Bohr’s model determine the radius of the first orbit of muon-proton system, if muon is 207 times heavier than electron -
(A)
0.53
(186)
ร
(B)
0.53
(186)2 ร
(C) 0.53 × 186 ร
(D) 0.53 × (186)2 ร
14. When an AC source E = E0 sin (50
3t) is used. The phase
difference between the current and emf is 3
. The circuit consists
only of RC, RL or LC series. Choose the correct pair -
(A) (B)
(C) (D)
15. A negatively charged particle is moving in a plane along a circular path in presence of an external magnetic field. Now suddenly an electric field is switched on such that the charged particle begins to move along a helical path with its axis parallel to the positive Y axis.
Which one of these combinations is possible ?
(A) E = E0 j , B = B0 j k (B) E = – E0 j , B = B0 j
(C) E = E0 j , B = – B0 j (D) E = – E0 j , B = B0 i j
16. Which circuit is correct verification of ohm's law ?
(A) (B)
(C) (D)
17. An ideal gas undergoes a cyclic process as shown in VT diagram, where the process CA is adiabatic. The process can also be represented by PT diagram as -
(A) (B)
(C) (D)
18. Two trains A & B are approaching each other with equal speeds of 130 m/s and sounding horns of frequency 120 Hz and 100 Hz respectively. A man standing in between the two trains starts running towards the train that is sounding horn at 100 Hz frequency with speed V. If he does not observ es any beats then find V in m/s ? Vsound = 330 m/s.
(A) 35 (B) 40
(C) 20 (D) 30
19. The mass number of an atom P is 240 and that of another atom Q is 80. If the radii of atom P is r then find the radii of atom Q ?
r
(A)
(B)
r
(C)
(D) r
20. For a particle executing SHM, the displacement is given by x = A sin t The curve which shows variation of potential energy with time and kinetic energy with displacement are respectively .
T T t
2
(A) 2, 4 (B) 1, 4
(C) 2, 3 (D) 1, 3
21. The resonance column method is used to calculate the speed of sound in air. The end correction for the tube is 2 cm. The 0.5 m of the air column resonates in third harmonic. If the length is changed such that the same tuning fork now resonates with fourth overtone, determine the new length
(A) 1.1 m (B) 1.54 m
(C) 2.1 m (D) 1.48 m
22. A particle is projected under gravity at some angle from the horizontal other than 90° . Its angular momentum remains constant about the -
(A) Point of projection (B) Projectile itself
(C) Highest Point (D) None of these.
23. A conducting current carrying loop is placed in x-y plane. If a non-uniform magnetic
field B = – B x2 kห , (where B is a cosntant) begins to act. The loop will tend to move
(A) Towards Positive x axis (B) Towards Negative x axis
(C) Towards Positive y axis (D) Remains stationary
24. A circular loop of radius 'a' and a square loop of side 'a' carrying equal currents i are oriented as shown in a region of uniform magnetic field directed outwards and perpendicular to the area enclosed by the loops. Arrange these in increasing order of potential energy ?
(I) (II)
(III) (IV)
(A) II, I, III, IV (B) I, II, IV, III
(C) I, II, III, IV (D) II, I, IV, III
25. 2Kg ice at –10°C , 1 Kg of ice at 0°C and 8.5 Kg of water at 20°C are mixed together. Then final amount of ice remaining is - [Given specific heat of ice = 0.5 cal/g°C, Specific heat of water = 1 cal/g°C, Latent heat of fusion of ice = 80 cal/g]
(A) 2 Kg (B) 2.5 Kg
(C) 1.5 Kg (D) 1 Kg
26. In the shown arrangement of the experiment of the meter bridge if AC corresponds to null deflection of galvanometer and its value is X. Now when a resistor 'R' is added between E and A, let X' ie AC' be new null deflection then...
(A) X' X (B) X' > X
(C) X' = X (D) X' X
27. A power source has two terminals A & B
A circular loop having resistance R is connected with the terminals of power source as shown. Arrange them in increasing order of power dissipation -
(i) A B (ii) A
B
(iii) A B (iv)
B
(A) iii, i, ii, iv (B) i, iv, ii, iii
(C) i, iv, iii, ii (D) iv, i, ii, iii
28. A nucleus of mass number 264 is at rest initially and emits two -particles as shown. If Q value of reaction is 9 Mev. Calculate the total kinetic energy of the particles released.
(A) 8.9 Mev. (B) 7.9 Mev.
(C) 9.1 Mev. (D) 9 Mev.
MAIN EXAMINATION
1. The N+1 divisions on the main scale of a Vernier callipers coincides with N + n divisions on the Vernier scale. If each division of main scale is of b units and the least count of the Vernier callipers is C units then calculate n ?
2. The energy of the incident electrons required to produce K characteristic X-rays from a target material is 20 KeV. Find the atomic number of the target material used to produce X-rays ? Given :
Rydberg constant R = 1.1 × 107 m–1 ; Planks constant h = 6.6 × 10–34 J-s
3. Two resonance tubes A and B have diameters 5cm and 10cm respectively. The air column in pipe A resonates with tuning fork of frequency 320 Hz. When the minimum length of air column is 20cm. Find the minimum length of air column of pipe B such that it also resonates with the same frequency ?
4. An insulated box containing a mixture of 2 mole of H2 and 1 mole of He is moving with some speed. It is suddenly stopped and as a result the temperature of the mixture of gases rises by 8ยบC. Find the speed of the box ?
5. Two long tubes of radius a and b are used to form soap bubbles. The one end
of each of the tubes are first dipped in soap solution having surface tension T V
and then air is blown from the other end of the tubes with speeds v and 2v respectively. Determine the ratio of the volumes of the soap bubbles formed?
6. Determine the resistance r for which the potential across the point A and B is 4 V ?
Tube Soap
bubble
7. A radioactive element decays by emission. A subatomic particle detector measures 0.75 n particles in 3 sec. and 0.25 n particles in the next 3 sec. Find the half life of the radioactive element.
[Given: ๐n3 = 1.0986; ๐n2 = 0.6931]
8. A particle of mass m is moving in a circle of radius 2R with constant speed v and starting from point (5R, 0) at t = 0 with its centre at (3R, 0). Now simultaneously a man starts moving from (R, 0) with same constant speed in a circle of radius R with origin as centre. Calculate the linear momentum of particle with respect to man as a function of time.
9. For the given lens determine the focal length of the lens. If the radius of curvature of both surfaces is R.
air air
10. In photoelectric experimental setup, photons of energy 5eV and intensity 10–7 W/m2 is incident on a target material having work function 4eV. It is observed that the saturation current is = 2A. Now the same target material was used in another experimental set-up where photons of energy 10eV having intensity 4 × 10–7 W/m2 were incident.
(a) Determine the saturation current in the experiment.
(b) Draw the graph between anode potential and current.
11. 5 charges of magnitude q each are placed as shown. The four positive charges from a square base of side ‘a’. The fifth charge –q is placed at distance 2a from each of the other four charges. Find the work needed to dismantle the system.
12. A tunnel is made from the surface of earth to its centre the mass of the earth be M and radius R. From the centre of earth a particle of mass m is projected with a speed which is equal to the escape velocity from the surface of earth find to what maximum height does the particle rise above the surface of earth ?
13. Two dipoles each having mass m and dipole moment P are placed along the x-axis far apart with → pointing
along the positive x-axis for both the dipoles. They start moving towards each other find the velocity of the dipoles when they are d distance apart. Find the force of interaction between the dipoles ?
14. An infinitely long wire carrying current = 0 sin t is placed parallel to the side PR of a square loop of side ‘a’ at a distance ‘a’ from it. The square conducting loop has a capacitor of capacitance C. Calculate the maximum charge that can be stored in the capacitor ?
15. Two rings of radius R and 4R and having uniformly distributed charge Q and 2Q respectively are mounted at equal distance d from the centre of the rod. The rod is suspended at its ends by two strings. The masses of the two rings are equal. If a vertical magnetic field is switched on and simultaneously the two
rings are rotated with angular velocity & respectively. Such that the
tension in the two strings remains unchanged then calculate the ratio of the
1
angular velocity 2 with which they need to be rotated ?
16. The tank shown has two similar capillary tubes P and Q but the length of capillary Q is twice that of capillary P. If the volume flow rate from the two capillary P & Q are 2 × 10–6 m3/s and 6 × 10–6 m3/s respectively then calculate the velocity of liquid flow at point O of liquid when the capillary Q is detached. Consider the size of the orifice at O to be small compared to area
of tank.
17. A string of length ‘L’ is tied between two supports. Its mass per unit length is and it vibrates forming 3 loops with maximum amplitude ‘a’. If the tension in the string is T, compute the total oscillation energy of the string?
18. A prism of refracting angle 45ยบ is coated with a thin film of transparent
material of refractive index 2.5 on the face AC of prism. A light of wavelength A
5200 ร
is incident on face AB such that angle of incidence is 60ยบ. Calculate :
(a) angle of emergence and (b) The minimum thickness of coating on face AC such that the light emerging from face has minimum intensity ?
B C
Refractive Index of prism = .
19. A mass m2 attached to a spring is moving along the positive x-axis with
speed V0 and when m2 reaches origin the spring strikes a mass m1 at t = 0 and sticks to it. Now both the masses connected with spring move
together. If velocity of mass m2
is given as V = V0
– A sint where A and
are constants. Find the velocity of the first block as a function of time.
Find the magnitude of the ratio of acceleration of masses ? x
20. An insulated cubical box has two partitions one has an electric coil and through the other partition water is passed. The coil maintains the temperature of top end of a conducting plate at 527ยบC. The conductivity of plate is 200 W/mk and its thickness is 1cm. The water enters at the bottom of the container at 7ยบC and leaves from the top at 27ยบC. Determine the rate of flow of water.
(Area of the conducting plate = 0.5 m2 , Cwater = 4200 J/kg°C)
ANSWER KEY TEST PAPER (PHYSICS) SCREENING EXAMINATION
1. (A) 2. (B) 3. (D) 4. (A) 5. (B)
6. (A) 7. (C) 8. (D) 9. (C) 10. (B)
11. (D) 12. (C) 13. (A) 14. (C) 15. (B)
16. (C) 17. (A) 18. (D) 19. (A) 20. (A)
21. (B) 22. (B) 23. (A) 24. (A) 25. (D)
26. (D) 27. (B) 28. (A)
MAIN EXAMINATION
1. n =
200
b Nc b c
2. Z = 45 3. 18.5 cm. 4. 329 m/s. 5. 64.
sin Vt sin Vt หi cos Vt cos Vt หj
6. 3
7. 1.89 sec 8. L – L = m V
P m R
2R 2R
R
R (2 2 )(kq2 )
9. f =
1 2 2
10. = 8A 11. W = a
qP C a
๐n 2
12. r = R. 13. V =
, F = 2 0 d3
14. qmax
= 0 0
4
15.
1
2 = 32 16. V = 10.95 m/s. 17. E =
92a2T
4L
18. (a) angle of emergence = 0 (b) t = 520 ร
.
19.
a1 m1 ; V = m2
A sin t 20. 59.5 kg/s.
a2 m2 1 m1
Comments
Post a Comment