Stage-1- Test Paper-3-Physics
SCREENING EXAMINATION
Time : 1.00 Hr Max. Marks : 84
GENERAL INSTRUCTIONS
1. This question paper has 28 objective type questions. Each question has four choices (A), (B), (C) and (D) out of which only one is correct.
2. For each question you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
Directions : Select the most appropriate alternative A, B, C and D in questions 1-35.
1. Which of the following groups do not have same dimensions
(A) Young’s modulus, pressure, stress (B) work, heat, energy
(C) electromotive force, potential difference, voltage(D) electric dipole, electric flux, electric field.
2. The wavelength of K X-ray of an element having atomic number z = 11 is . The wavelength of K X-ray of another element of atomic number z is 4 Then z is
(A) 11 (B) 44
(C) 6 (D) 4
3. Three large parallel plates have uniform surface charge densities as shown in the figure. The electric field at point P is -
(A) –
4 kˆ (B)
0
4 kˆ
0
(C) – 2 kˆ
0
(D) 2 kˆ
0
4. Figure shows object O. Final image is formed after two refractions and one reflection is also shown in figure. Find the focal length of mirror. (in cm)
(A) 10 (B) 15
(C) 20 (D) 25
5. A block of mass m is held fixed against a wall by applying a horizontal force F. Which of the following option is incorrect.
(A) friction force = mg (B) normal will not produce torque
(C) F will not produce torque (D) normal reaction = F
6. The velocity displacement graph of a particle moving along a straight line is shown. The most suitable acceleration-displacement graph will be
(A) (B)
(C) (D)
7. In Young’s double slit experiment an electron beam is used to form a fringe pattern instead of light. If speed of the electrons is increased then the fringe width will :
(A) increase (B) decrease
(C) remains same (D) no fringe pattern will be formed
8. In Young’s double slit experiment maximum intensity is then the angular position where the intensity
becomes 4
(A) sin–1 d
is :
(B) sin–1 3d
(C) sin–1 2d
(D) sin–1 4d
R
9. A disc has mass 9m. A hole of radius 3 is cut from it as shown in the
figure. The moment of inertia of the remaining part about an axis passing through the centre ‘O’ of the disc and perpendicular to the plane of the disc is :
(A) 8 mR2 (B) 4 mR2
40
(C) 9
37
mR2 (D) 9
mR2
2
10. The ratio of magnitude of focal length of a thin convex and thin concave lens is 3 and equivalent focal length of their combination is 30 cm. Then their focal lengths respectively are
(A) –10, 15 (B) 75, 50
(C) 10, – 15 (D) – 75, 50
11. Water is filled in a container upto height 3m. A small hole of area ‘a’ is punched in the wall of the container at
a
a height 52.5 cm from the bottom. The cross sectional area of the container is A. If
v is the velocity of water coming out of the hole)
(A) 48 (B) 51
(C) 50 (D) 51.5
= 0.1 then v2 is (where
A
12. A particle moves in circular path with decreasing speed. Which of the following is correct
→ →
(A) L is constant (B) only direction of L is constant
→
(C) acceleration a is towards the centre (D) it will move in a spiral and finally reach the centre
13. Helium nuclei combines to form an oxygen nucleus. The binding energy per nucleon of oxygen nucleus is if m0 = 15.834 amu and mHe = 4.0026 amu
(A) 10.24 MeV (B) 0 MeV
(C) 5.24 MeV (D) 4 MeV
14. An infinitely long cylindrical conducting rod is kept along + Z direction. A constant magnetic field is also present in + Z direction. Then current induced will be -
(A) 0 (B) along +Z direction
(C) along clockwise as seen from + Z (D) along anticlockwise as seen from + Z
15. A photon of 10.2 eV energy collides with a hydrogen atom in ground state inelastically. After few microseconds one more photon of energy 15 eV collides with the same hydrogen atom. Then what can be detected by a suitable detector.
(A) one photon of 10.2 eV and an electron of energy 1.4 eV
(B) 2 photons of energy 10.2 eV
(C) 2 photons of energy 3.4 eV
(D) 1 photon of 3.4 eV and one electron of 1.4 eV
16. Three graphs marked as 1, 2, 3 representing the variation of maximum emissive power and wavelength of radiation of the sun, a welding arc and a tungsten filament. Which of the following combination is correct
(A) 1- bulb, 2 welding arc, 3 sun (B) 2- bulb, 3 welding arc, 1 sun
(C) 3- bulb, 1 welding arc, 2 sun (D) 2- bulb, 1 welding arc, 3 sun
17. In the figure shown the current through 2 resistor is
(A) 2A (B) 0 A
(C) 4 A (D) 6A
18. In which of the following phenomenon heat convection does not take place
(A) land and sea breeze
(B) boiling of water
(C) heating of glass surface due to filament of the bulb
(D) air around the furnace
19. An ideal gas is filled in a closed rigid and thermally insulated container. A coil of 100 resistor carrying current 1A for 5 minutes supplies heat to the gas. The change in internal energy of the gas is
(A) 10 KJ (B) 20 KJ
(C) 30 KJ (D) 0 KJ
20. An uncharged capacitor of capacitance 4µF, a battery of emf 12 volt and a resistor of 2.5 M are connected in series. The time after which vc = 3vR is (take 𝑙n2 = 0.693)
(A) 6.93 seconds (B) 13.86 seconds
(C) 7 seconds (D) 14 seconds
21. When the pressure is changed from p = 1.01 × 105 Pa to p = 1.165 × 105 Pa then the volume changes by
1 2
10% keeping temperature constant. The bulk modulus of medium is :
(A) 1.55 × 105 Pa (B) 0.0015 × 105 Pa
(C) 1.4 × 105 Pa (D) 1.01 × 105 Pa
22. A simple pendulum has time period T1. When the point of suspension moves vertically up according to the
T 2
equation y = kt2 where k = 1 m/s2 and ‘t’ is time then the time period of the pendulum is T
then 1 is
T2
5
(A) 6
6
(C) 5
11
(B) 10
(D) 5 4
23. A galvanometer has resistance 100 and it requires current 100µA for full scale deflection. A resistor 0.1 is connected to make it an ammeter. The smallest current required in the circuit to produce the full scale deflection is
(A) 1000.1 mA (B) 1.1 mA
(C) 10.1 mA (D) 100.1 mA
24. 2 litre water at 27°C is heated by a 1 kW heater in an open container. On an average heat is lost to surroundings at the rate 160 J/s. The time required for the temperature to reach 77°C is
(A) 8 min 20 sec (B) 10 min
(C) 7 min (D) 14 min
25. A spherical body of area A, and emmissivity e = 0.6 is kept inside a black body. What is the rate at which energy is radiated per second at temperature T
(A) 0.6 eAT4 (B) 0.4 eAT4
(C) 0.8 eAT4 (D) 1.0 eAT4
26. An open organ pipe is in resonance in its 2nd harmonic with a tuning fork of frequency f1. Now it is closed at one end. If the frequency of the tuning fork is increased slowly from f1 then again a resonance is obtained when the frequency is f2. If in this case the pipe vibrates in nth harmonic then
3
(A) n = 3, f2 = 4 1
5
(B) n = 3, f2 = 4 1
5
(C) n = 5, f2 = 4 2
3
(D) n = 5, f2 = 4 1
27. 1 calorie is the heat required to increase the temperature of 1 gm of water by 1°C from
(A) 13.5°C to 14.5°C at 76 mm of Hg (B) 14.5 °C to 15.5°C at 760 mm of Hg
(C) 3.5°C to 4.5°C at 76 mm of Hg (D) 98.5°C to 99.5°C at 76 mm of Hg
28. A tuning fork of 512 Hz is used to produce resonance in a resonance tube experiment. The level of water at first resonance is 30.7 cm and at second resonance is 63.2 cm. What is the maximum error in measuring speed of sound :
(A) 51.2 cm/sec (B) 204.8 cm/sec
(C) 153.6 cm/sec (D) 102.4 cm/sec
MAIN EXAMINATION
Time : 2.00 Hrs Max. Marks : 60
GENERAL INSTRUCTIONS
1. There are 18 questions in this paper.
2. Question number 1 to 8 carry 2 Marks each and question number 9 to 16 carry 4 Marks each and question number 17 to 18 carry 6 Marks each.
3. The use of Arabic numerals (0,1,2, 9) only is allowed in answering the questions irrespective of the
language in which you answer.
1. A train is passing a stationary observer at station with constant velocity. If the frequency observed by the person during its approach and recession are 2.2 kHz and 1.8 kHz respectively. Then find the velocity of train if the velocity of sound in air is 300 m/s.
2. Side of a cube is measured with the help of vernier calliper. Main scale reading is 10 mm and vernier scale reading is 1. It is known that 9 M.S.D. = 10 V.S.D.. Mass of the cube is 2.735 g. Find density of the cube upto appropriate significant figure.
3. Find height difference H of the liquid column in two limbs when the U tube is rotated with angular speed . (while diameter of the tube d << L)
4. What is the minimum angle of incidence of incident ray at the surface AB so that the light is totally reflected at the surfaces AB and CD.
5. A rod of mass M, length L hinged at its one end is in vertical equilibrium position. A bullet of mass m, moving with velocity v strikes the lower end of the rod and gets embedded into it. Find the angular velocity of the rod just after the collision.
6. A bubble of conducting liquid is charged to potential v, it has radius a and thickness t << a. It collapses to form a droplet. Find potential of the droplet.
7. A solid cylinder of mass ‘m’ rolls without slipping on a fixed long inclined plane inclined at an angle with horizontal. Find the linear acceleration of the centre of mass of the cylinder.
8. A transverse wave travelling in a string produces maximum transverse velocity of 3 m/s and maximum transverse acceleration 90 m/s2 in a particle. If the velocity of wave in the string is 20 m/s. Determine the wave form?
9. Two rods of mass M and length L are placed as shown in figure. If the system is in equilibrium then find the magnitude and direction of frictional force at the points of contact A and B ?
10. The potential energy of a mass ‘m’ is given by the following relation U = E0
for 0 x 1 = 0 for x > 1.
If and are the de-Broglie wavelengths of the mass in the region 0 x 1 and for x > 1 respectively and
1
the total energy be 2E0 , then find the value of 2 ?
11. For the three values of resistances R namely R1, R2 and R3 the balanced positions of jockey are at A, B and C respectively. Which position will show most accurate result for calculation of X. Give reason. B is near the mid point of the wire.
12. In the given circuit the capacitor C is uncharged initially and switch ‘S’ is closed at t = 0. If charge on capacitor at time ‘t’ is given by equation
Q = Q (1 – e– t ). Find value of Q and ?
13. A metal target consist of large number of atoms (with each atom having number of neutrons is 30). The radius
4
ratio of the target atom to 2 is (14)
1/3.
(a) Find the atomic number of metal
(b) Find the frequency of K X-ray for that metal
(Given : Rydberg constant = 1.1 × 107 m–1 ; speed of light = 3 × 108 m/s.)
14. A block is performing SHM of amplitude ‘A’ in vertical direction. When block is at ‘y0’ (measured from mean position), it detaches from spring, so that spring con-
tracts and does not affect the motion of the block. Find ‘y0’ such that block attains maxi mum height from the mean position. (Given A 2 > g)
15. Current passing through a long solenoid having n turns per unit length is
= sin t. Find induced current through copper shell having resistivity
as shown in figure.
16. A mass of 1 kg at 20°C is given an energy 20000 J at 1 atmospheric pressure
(i) Find the change in temperature of mass. (ii) Find the work done by mass.
(iii) Find the increase in internal energy of mass.
{Given 1 atm = 105 N/m2, Specific heat capacity = 400 J/kg °C, density = 9000 kg/m3 , coefficient of cubical expansion = 9 × 10–5 /°C}
17. In the figure two triangular prisms are shown each of refractive index 3 .
(a) Find the angle of incidence on the face AB for minimum deviation from the prism ABC?
(b) Find the angle through which the prism DCE should be rotated about the edge passing through point C so that there should be minimum deviation from the system?
18. Relation for a Galvanometer having number of turns N, area of cross section A and moment of inertia is given as : = Ki where K is a positive constant and ‘ i ’ is current in the coil placed in the magnetic field B.
(i) Find K in terms of B, N and A
(ii) Find torsional constant of spring if a current
produces a deflection of 2
(iii) If an instant charge Q is flown through the galvanometer, find the maximum deflection in the coil.
A nswers
SCREENING EXAMINATION
1. (D) 2. (C) 3. (C) 4. (C) 5. (B) 6. (B) 7. (B)
8. (B) 9. (B) 10. (C) 11. (C) 12. (B) 13. (A) 14. (A)
15. (A) 16. (A) 17. (B) 18. (C) 19. (C) 20. (B) 21. (B)
22.
(C)
23.
(B)
24.
(A)
25.
(A)
26.
(C)
27.
(B)
28.
(B)
MAIN EXAMINATION
1. Vs = 30 m/s 2. 0.00265 3. H =
2𝑙2
2g
4. i > 60°
5. =
3mv
(M 3m) L
a 1/ 3
6. v = v 3 t
2gsin
7. a = 3
30 t 3 x
8. Equation of wave in string y = 0.1 sin
[where is initial phase]
9. f =
(M m)gcot 2
required friction 10.
11. Fractional error in x is least if (100 – 𝑙) 𝑙 is maximum and it is when 𝑙 = 50 cm.
12. Q0 =
R2 VC R1 R2
g
& =
(R1 R2 ) CR1R2
13. (a) 26 (b) 154875 × 1012 Hz
(0 na20cost) Ld
14. y0 = 2
15.
2R
16. (i) 50ºC (ii) 0.05 J (iii) 19999.95 J
17. (a) Angle of incidence = i = 60°
(b) For minimum deviation for the system, deviation from two prism will be zero and the two prism will form parallel slab
for this situation prism DCE is rotated in anticlockwise direction by 60°
18. = Q
STAGE SOLUTIONS TO TEST PAPERS (PHYSICS)
2
SCREENING EXAMINATION
1. Electric dipole = q × 2𝑙 = L1T1A1
Electric flux = E ds
= (F/q) ds =
M1L1T2 AT
× L2 = M1 L3 T–3 A–1
F
Electric field = q = M1L1T–3A–1
1
2. For K (z – 1)
1
(z – 1)
or (z 1)2
............(i)
1
4 (z 1)2
............(ii)
1 (z´1)2
z´1 1
4 = (z 1)2
z 1 = 2
2z´ – 2 = z – 1 2z´ – 2 = 11 – 1 = 10 z = 6
3.
Resultant electric field =
2 0 +
2
2 0 +
2 0 =
4
2 0 =
2
0 =
2 ( – kˆ )
0
4. For mirror
approximate distance of object
33.25
Apparent depth Real depth
= 15 + 4
× 3 = 39.93
rel
approximate distance of image from mirror
15 +
25 × 3 = 33.75
4
from mirror formula
1
– 33.75 +
1
39.9
= 1 ; f ~ 19 cm
f
5. From equilibrium, friction = mg N = F about centre of mass
= 0 mg a = torque due to normal
Normal will produce torque
since F passes through centre its torque is zero.
6. From the graph
v = v0 – mx
acceleration
dv
a = dt
dx
= – m dt
= – mv = – m (v0
– mx) = – mv0
+ m2x
i.e. slope positive
y axis intercept negative
h
7. On increasing speed of electron, de Broglie wavelength associated with it will decrease
mv .
D
Since fringe width = d
, so it will decrease.
8. when = 0 I = Imax =
I = 4I
I 2
where I1 = I2 = I0
Intensity of one slit I 0 = 4
Let angular position be where intensity becomes I/4
= +
+ 2 cos cos = –
1 = 2
4 4 4 4
2 3
2
Also 2 =
= 3 2 × = 3
d sin = 3
sin = 3d
= sin–1 3d
9. = –
where = (M.. of full disc about O)
= (M.. of small removed disc about O)
since mass area
R2
mass of cut disc 9
mass of total = R2
= 1 mass of cut disc = m
9
(9m)R2
R 2
3
2
2R
=
– m
(by theorem of parallel axis.)
0 2
3
9mR2
1 4
9mR2
mR2
8mR2
= – mR2 18 9 = – =
= 4mR2.
2
10.
Pconvex Pconcave
= – 3 =
2
fconcave fconvex
...............(1)
1
fconcave +
1
fconvex =
1
30 ..............(2)
concave convex
11. Continuity equation
av = AV Bernoulli’s equation
p0 v 2
2
1
p0 V 2
+ g(3) = + 2
1
+ g(.525)
2 (0.1)2 v2 – 2
v2 = g (.523 – 3) v2 = 50 (m/s)2.
→
12. Only direction of L (angular momentum) is constant because the direction of rotation is unchanged.
13. m = 4m – m
m = 0.176
binding energy per Nucleon = 0.176/16 amu = 10.24 meV
14. zero, as there is no flux change. [Normal to the rod is perpendicular to the field. = 0]
15. First photon will excite the atom to excited state, which when returning to ground state will emit a photon of energy 10.2 eV second photon will ionize the atom (13.6 eV will be used up in this process). The extra energy (=15 – 13.6 = 1.4 eV) will be carried by electron as its kinetic energy.
So a photon of energy 13.6 eV and an electron of energy 1.4 eV will be emitted.
16. According to Wien’s displacement law
1
mT = constant T max
from graph
max(2)
max(3)
T < T
< T3
the material having low temperature has the graph having lower peak.
17. From Kirchoff’s law, current in 2 is zero, because 2 resistance is not a part of closed circuit.
18. Bulb heats up by radiation process
19. U = Q = 12 × 100 × 5 × 60 J = 30 KJ
20. vc + vR= 12
vc +
vc = 12 v
3 c
= 9 volt
q
vc = C
CE(1 et / RC )
= C
= E (1 – e–t/RC)
9 = 12 (1 – e–t/4×2.5)
9 = 12 – 12e–t/10
1
3 = 12e–t/10 ; e–t/10 = 4
t
10 = 𝑙n4 = 2𝑙n2 = 2 × .693
t = 2 × 6.93 = 13.86
21. B = – P
V
V
(0.155 105 )
= 10
100
= + 0.155 × 106 = 1.55 × 105
22. T = 2 = 2
d2y
upward acceleration dt2
= 2k = 2 × 1 = 2 m/s2
Acceleration w.r.t. point of suspension = 12 m/s2
T
T 2 6
T = 2
1
T2 =
1
T2
= 5 .
23. i = ig + is (1)
igG = isS (2)
from (1) & (2) (putting i = 0.1 mA, G = 100, S = 0.1) we have i = 100.1 mA
24. Net heat given/sec = 1000 – 160
= 840 J/S
if it takes a time t then 840 t = 2000 × 4.2 × (77 – 27)
t = 500 sec = 8 min 20 sec.
25. As from the four options given, no option is correct.
dQ
But if we assume ‘e’ as the symbol of Stephen’s constant then dt
= 0.6 eA T4
26. f
= 2v
= v f
= nv As given nv > v
1 2L L
2 4L
4L L
n > 4 n = 5
27. Clear from the definition.
28. In resonance tube, for first resonance, 𝑙1 + x = 4
3
For second resonance, 𝑙2 + x = 4
𝑙 – 𝑙 = or 2(𝑙 - 𝑙 ) = v or v = 2f (𝑙 – 𝑙 )
2 1 2 2 1 f 2 1
v = 2f(𝑙 + 𝑙 ) , for maximum error
v = 2 × 512 (0.1 + 0.1)
v = 204.8 cm/s maximum possible error in speed = 204.8 cm/s
MAIN EXAMINATION
300
1. Apparent frequency during the approach 1.8 × 103 = 300 V
f
300
........(1)
Apparent frequency during the recession 2.2 × 103 = 300 V f
.(2)
By solving above two equations V = 30 m/s
(V.S. M.S.)
2. Least count =
V.S.
Least count = 0.1 mm
length of side of cube = M.S.R. + V.S.R. × least count
= 10 + 1 × 0.1 = 10.1 mm
mass
density = volume
2.735
= (10.1)3
= 0.0026546
using significant figures the correct answer would be 0.00265
3. Applying Newtons law on liquid in limb AB
L
2𝑙2
g H A = A L 2
2
H = 2g
4. For total internal reflection (TIR)
at AB i > 45°, for TIR at CD i > 60°, so for TIR at both surfaces i > 60°
5. Initial angular momentum about fixed point = mvL
ML2 2
final angular momentum = = mL
where is moment of inertia of the system about the fixed point and is angular velocity about the fixed point. angular momentum before collision = angular momentum after collision
M
mv 3mv
mLv = L2 3 m = M
= (M 3m) L
L
3
m
6. Conserving volume of liquid 4a2 t =
4 r 3
3
r = (3a2 t)1/3
charge on the droplet = charge on bubble = q
kq
v = a
, v = kq
r
v
v
= a =
r
a (3a2t)1/ 3
a 1/ 3
= 3t
a 1/ 3
v = v 3 t
7. Applying NLM mg sin – f = ma (1)
2
torque equation about centre of mass fr = (2)
a = R for no slipping (3)
by solving above three equations
a =
2gsin
3
8. Maximum particle velocity v
max
= A = 3 m/s
Maximum particle acceleration amax
= 2 A = 90 m/s2
3 3
amax
= vmax
= × 3 = 90 m/s2 = 30 s–1 A =
= 30
= 0.1 m
K = v
30 3
= 20 = 2
30 t 3 x
[where v is velocity of wave]
is initial phase]
Equation of wave in string y = 0.1 sin
2
[where
9. Applying Newton’s law in vertical direction on system 2Mg + mg = 2N (1)
applying equation of torque on rod AC about point ‘C’ for rotational equilibrium = 0
f L sin + Mg
L cos = NLcos (2)
2
Mg Mg mg Mg
f = N cot –
cot
2
f =
cot –
2
2 cot xc
(M m)gcot
f = 2
required friction
10. For 0 x 1, KE = 2E – E = E
for x > 1 , KE = 2E0
1
2 =
h / P1 h / P2
P2
= P1 = =
11. From Wheat stone bridge
x 𝑙
R = 100 𝑙
x =
R𝑙 (100 𝑙)
Taking log on both sides loge x = loge R + loge 𝑙 – loge (100 – 𝑙)
dx d𝑙
(d𝑙)
100 d𝑙
differentiating x = 𝑙
– (100 𝑙)
= (100 𝑙)𝑙
fractional error in x is least if (100 – 𝑙) 𝑙 is maximum and it is when 𝑙 = 50 cm.
12. By KVL in loop ABCFA
q
V – i R1 – C = 0 (1)
By KVL in loop CDEFC
q
– (i – i1) R2 + C
= 0 ...(2)
V q 1 q
by equation (1) and (2) eliminate i – R + i R + = 0
2 C R1 1 2 C
i =
dq – R2 V +
q
R + R
dq q
+ = 0
1 dt
R1 CR1 2
2 dt C
R 1 R V dq
t R2dq
Q R dq
q 2
– 2 = –
R2 dt =
= 2
CR1 C R1 dt
0 0 q R2
1 R2 V
aq b
0
R 1 R V
CR1 C R1
R aQ b
b at
[ where a = 2 and b = 2 ] – t =
2 ln
Q =
(1 e
R2 )
CR1 C R1 a b a
R2 VC
Q = R1 R2
& =
(R1 R2 ) CR1R2
A 1/ 3
13. (a) Using R = R (A)1/3 (14)1/3 =
A = 14 × 4 = 56
0
Z = A – N = 56 – 30 Z = 26
4
1 1 1 c 1 1
(b)
= R (Z – 1)2 12 22
=
= Rc (Z – 1)2 12 22
3 3
= 1.1 × 107 × 3 × 108 × (26 – 1)2 4 = 1.1 × 3 × 625 × 4 × 1015
= 9.9 × 625 × 25 × 1013 = 154875 × 1012 Hz
14. v2 = 2 (A2 – y2) (1)
v 2
h = 2g
dh
+ y h =
2(A 2 y2 )
2g + y
dy = 0 (for maximum height)
dh 2 g
dy = – (2y) + 1 = 0 y = 2
15. B inside the solenoid = ni
magnetic flux through copper shell =
d
ni × a2 B outside solenoid = 0
di
induced emf = dt (
ni a2) =
n a2
dt
= n a2
cos t
current =
induced emf Resis tan ce
0na20 cos t
= (2R)
(Ld)
(0 na20cost) Ld
= 2R
16. By st law of thermodynamics : Q = u +
20000 = m S T + P V
= m S T + P V T = m S T + P .
m T
T =
20000
=
20000
20000
=
~ 50°C
mS Pm
1 400
105 9 105 1
9000
400
1
1000
m 1 1
Work done by mass = P T = 1000 × 50 = 20 J
u = 20000 –
1
20 = 19999.95 J
17. (a) = i + e – r – r
for minimum deviation r1 = r2 = 30° and i = e
min
= 2i – 60° =
sin i
= sin 30
; sin i = 3 2
i = 60° Angle of incidence = i = 60°
(b) For minimum deviation for the system, deviation from two prism will be zero and the two prism will form parallel slab for this situation prism DCE is rotated in anticlockwise direction by 60°
18. (i) Torque in coil = NiAB (assuming) K = NAB
(ii) from NiAB = C where C = torsional constant of spring.
C =
N0 AB
/ 2
2NAB0
=
(iii) Angular impulse = change in angular momentum
dt = L or BiNA dt = – 0
=
BNAQ [ idt
= ]
This is initial angular speed for further motion Now, by energy conservation
[Note : after this it can also be solved by using equation – C =
d
d ]
1 1 1
BNAQ 2 1
2 =
2
C2
2
2
= C 2 = Q
2
STAGE
3
Time : 1.00 Hr
SIMILAR TEST PAPERS (PHYSICS)
SCREENING EXAMINATION
Max. Marks : 84
GENERAL INSTRUCTIONS
1. This question paper has 28 objective type questions. Each question has four choices (A), (B), (C)
and (D) out of which only one is correct.
2. For each question you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded.
1. Which of the following sets have same dimensions (symbols has usual meaning)
(A) Velocity ,
1 , E B
(B) Dipolemoment , Electric potential , E.M.F.
(C) (C)
L , LC , RC (D) Pressure, Viscosity, Planks constant
R
2. The wave length of K X-ray of an element having atomic number z = 16 is . The wavelength of K X-rays of another element of atomic number z = 21 is :
(A) 3/4 (B) 5/16
(C) 9/15 (D) 9/16
3. Four large parallel plates have uniform surface charge density. The plates lie
in the YZ plane. Find the electric field intensity at point P ?
(A)
3 ˆi 20
(B) (B)
3 ˆi
20
(C) –
3 ˆj
20
(D) Zero
4. A glass slab of thickness 20 cm and of refractive index 1.5 is placed in front of a concave mirror. The object ‘O’ and its final image ‘I’ after two refractions and one reflection is shown. Determine the focal length of the mirror ?
(A) f = 25.5 cm (B) f = 20.5 cm
(C) f = 30.5 cm (D) f = 35.5 cm
5. Two blocks of mass m & 2m are held fixed against a wall by applying horizontal force F which of the following option is correct -
(A) Friction force between 2 m & wall is 2 mg
(B) Friction force between blocks = 2 mg
(C) Friction force between wall & 2 m block is 3 mg
(D) Friction force between blocks = F
6. The given graph shows the variation of velocity with displacement, which oneof the graphgiven belowcorrectly representsthe variation of acceleration with displacement -
(A) (B)
(C) (D)
7. In Young’s double slit experiment an electron beam is used to form a fringe pattern instead of light. If accelerating potential of electron beam increased to four times then the fringe width.
(A) Doubled (B) halved
1
(C) become four times (D) become 4
times
8. In Young’s double slit experiment maximum intensity is I, then the angular position where the intensity becomes I/2 is -
(A) sin–1 2d
(B) sin–1 2D
(C) sin–1 2d (D) sin–1 4d
9. From the semi circular disc of radius R and mass 8 m. A small disc of radius R/2 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc
and passing through O is -
R2
(A) m 8
(B) mR2
R2
(C) 3m 8
R2
(D) m
4
4
10. The ratio of magnitude of powers of a thin convex and a thin concave lens is 5
their combination is 50 cm then their focal lengths respectively are - (A) 10, – 12.5 (B) 20, –25
(C) –20, 25 (D) –10, 12.5
and equivalent focal length of
11. A hemispherical tank of radius 20 cm, completely filled with a liquid, through a small hole of radius 2 cm at its bottom liquid discharges. Then V2 is (where V is the velocity of water coming out of the hole) -
(A) 4 m2/s2 (B) 40 m2/s2
(C) 3.8 m2/s2 (D) 4.6 m2/s2
12. A particle moves in a circular path with increasing speed, choose the correct statement -
(A) Angular momentum is towards the centre.
(B) Angular acceleration is radial
(C) Angular velocity is along the axis of revolution
(D) The Linear acceleration is along the tangent of circle.
13. Binding energy per nucleon for 56 Fe is -
[mn = 1.008665 amu, mp = 1.007825 amu , mass of Fe nucleus = 55.93492]
(A) 8.79 Mev (B) 6.79 Mev
(C) 7.39 Mev (D) 11.32 Mev
14. An infinitely long wire carrying current I is placed along y axis and square loop of side a at distance r from wire is displaced along y axis with velocity V then induced current in the loop (Resistance of loop is R)
o a2 VI
(A)
2R
(B) Clock wise in the loop
(C) Anti clock wise (D) Zero
15. A photon of 12.75 e.V. energy collides with a hydrogen atom in ground state inelastically, then what can be detected -
(A) Only one photon of 12.75 e.V.
(B) Either one photon of 12.75 or more photon of smaller energy
(C) One electron of energy 0.85 e.V.
(D) One photon of 10.2 e.V. and an electron of energy 1.4 e.V...
16. The emission spectrum of a black body at two different tempera-
tures are shown by curve P and Q as shown in figure. The ratio of the area under the two curves P and Q will be -
(A) 1 : 16 (B) 4 : 9
(C) 81 : 256 (D) 16 : 81
17. In the figure shown the current through 10 resistance is : (A) 3A (B) 1.02 A
(C) 1 A (D) zero
18. In which of the following phenomenon heat conduction can take place -
(A) Heat transfer from the bulb to the surrounding. (B) Heat transfer through boiling water.
(C) Heat transfer through mercury liquid. (D) Air around the furnace
20V
19. An ideal gas is filled in a closed rigid ideal conducting container. A coil of 60 resistor carrying current 1A for 5 minutes supplies heat to the gas. The change in internal energy of the gas is -
(A) 3.6 kJ (B) 10 kJ
(C) 2 kJ (D) 0 kJ
20. An uncharged capacitor 10µF, a battery of emf 12 volt and a resistor 2 M are connected in series. The time after which potential at capacitor and resistance become equal (take 𝑙n2 = 0.693) -
(A) 13.86 sec. (B) 6.93 sec.
(C) 3.46 sec. (D) 10.395 sec.
21. When the pressure is changed form P1 = 1.01 × 10 Pa to P = 1.26 × 105 Pa of a medium of bulk modulus
5
5 × 105 Pa then percentage change in volume keeping temperature constant is.
(A) 5 % (B) 0.5 %
(C) 15 % (D) 10 %
22. A simple pendulum has time period T1. When the point of suspension moves vertically up according to the
T 2
equation y = 4kt where k = 1 m/s2 and ‘t’ is time then the time period of the pendulum is T
then 1 is
T2
7
(A) 5
2
(B) 5
(C) 1 (D) 4
23. A galvanometer has resistance 100 and it requires 10 m A current for full scale deflection, then resistance connected to make it an ammeter for measuring current up to 10 A is
(A) 100 (B) 1
(C) 1.01 (D) 0.1
24. Find the time taken by a 1 kW heater to raise temperature of 10 kg of a liquid of specific heat capacity 1260 J/Kg°C from –20°C to 32°C. Assume the efficiency of the heater to be 60% and that 25% of the heat evolved is lost into the atmosphere -
(A) 18.2 min. (B) 24.3 min.
(C) 36.4 min. (D) 12.8 min.
25. A cubical block of side a and emissivity e = 0.5 is kept inside a black body what is the rate at which energy is radiated per second at temperature T°C (body radiates energy uniformly, = stephen's constant)
(A) 0.5a2T4 (B) 0.3a2T4
(C) 3a2T4 (D) 3a2(T + constant)4
26. A closed organ pipe is in resonance in 4th harmonic with frequency f1 now one third length of organ pipe is cut from closed side and remaining pipe is in resonance again in 3rd harmonic with frequency f2 . Choose the correct option -
(A) f2 > f1 (B) f1 = f2
(C) 3f2 = 4f1 (D) 2f2 = 9f1
27. Specific heat of boiling water at atmospheric pressure is -
(A) 1 calorie/gm (B) 0.5 calorie/gm
(C) 530 calorie/gm (D) None of the above
28. A tuning fork of 512 Hz is used to produce resonance in a resonance tube experiment. The level of water at first resonance is 28.07 cm and at second resonance 44.13 cm. What is the maximum error in the measur- ing of wavelength of sound.
(A) 0.02 (B) 0.2
(C) 0.04 (D) 0.06
MAIN EXAMINATION
Time : 2.00 Hrs Max. Marks : 60
GENERAL INSTRUCTIONS
1. There are 18 questions in this paper.
2. Question number 1 to 8 carry 2 Marks each and question number 9 to 16 carry 4 Marks each and question number 17 to 18 carry 6 Marks each.
3. The use of Arabic numerals (0,1,2, 9) only is allowed in answering the questions irrespective
of the language in which you answer.
1. A station master is sounding a horn of a given frequency. An observer in a train which is approaching the station with constant velocity hears a frequency of 4 Hz and of 2.5 Hz after the train crosses the station. Taking the velocity of sound in air as 300 m/s, calculate the velocity of train and the frequency of the horn at the station ?
2. A vernier calliper is used to measure the volume of an sphere. The least count of the calliper is 0.2mm and while measuring the diameter of sphere the main scale reading is 20mm and vernier scale reading is 4. Find the volume of the sphere with appropriate significant figure ?
3. The shown U-tube is rotated about the axes parallel to the liquid columns in two limbs and at distance 'L' from the left limb with angular velocity . Determine the difference of the heights in the two limbs ?
4. Determine the minimum angle of incidence of the incident ray at face PQ such that the ray is totally internally reflected at surfaces PQ and RS. The QS surface is silvered?
R
n = 1
S
5. A rod of mass M and length L is hinged at its centre of mass. Two masses each of mass m strike with equal speed V as shown and come to rest thereafter. Determine the angular velocity of the rod after the collision ?
6. Two identical bubbles of radius r and thickness t collide together forming a liquid droplet. If the charges on the two bubbles are q and 2q, determine the potential of the droplet?
7. A ring and a disc of same mass 'm' and radius 'R' begin to roll down an incline without slipping. Find the ratio of the linear speeds of the two when they reach the bottom of incline plane. Consider that both are released from the incline plane separately ?
8. The velocity of a transverse wave form in a string is given as V = 10 cos (t + )m/s and the maximum transverse acceleration of particles is 500 m/s2. Determine the amplitude of the particle?
9. A ladder has two legs each of mass M connected by a frictionless hinge H. Two men each of mass m start climbing the ladder. Determine the minimum friction coefficient between the ladder and the ground such that the two men can safely reach the mid-point of the legs of the ladder. Consider the length of each of the legs as 'L' ?
x
10. The potential energy of a particle of mass m in the region x > 1 is given by the relation U = E
x – 1 .
0
If is the de-Broglie wavelength of the particle at x = 2 and its total energy being 3E , then determine
0
?
11. Three unknown resistances R1, R2, R3 are placed at position x one after another and the balanced positions of jockey obtained are at P, Q and R respectively. The distances of P, Q, R from ‘O’ are 10cm, 30cm, 90 cm respectively and OA = 1m. The resistance R in the circuit is of 10 Determine the ratio of the resistances R1 : R2 : R3 ?
12. The circuit with the capacitor C and equal resistances R is shown in the figure. Determine the time constant of the circuit ?
13. Two target elements A and B used in an X-ray tube have their radius ratio (2)1/3 with the lighter nuclei having mass number 52. The atoms of elements A and B have number of neutrons 63 and 21 respectively
(a) Determine their atomic number
(b) Determine the ratio of the frequency of K X – rays produced by A and B?
14. A block of mass m is attached to one end of a spring with the
other end of spring attached to the ceiling. The block performs SHM of amplitude A and frequency in vertical direction. If the mean position is 2A distance above the floor and the spring is cut when the block is at mean position and moving upwards. Determi the maximum height attained by the mass from the ground andthe velocity with which it hits the ground ? (Given g = 2A).
15. A long solenoid having n number of turns per unit length (and radius a) is shown. The current passing
through the solenoid is = cost. A copper coil of radius ‘b’ is placed along the axes of the solenoid
with the angle between the axes of coil and solenoid being 60º. Determine the induced current in coil, if its resistance is R ?
16. A wire having mass per unit length 0.2 kg/m and length 1m and with cross-sectional area 1cm2 is given 1000 J of heat energy at 2 atm. pressure. Determine the rise in its temperature and the work done by the mass, if it is assumed that change in its cross-sectional area is negligible?
GiveSpecific heat capacity 600 J/ Kg º C
Coefficient of linear expansion 3 10–5 /º C
17. (a) Determine the total deviation produced by the equilateral prism, if the light ray undergoes total internal reflection at the face AC of the prism ? (b) Find out the angle of incidence and angle of emergence if the ray passes the prism parallel to the base.
18. A moving coil galvanometer has 20 turns with cross-sectional area 9 cm2 placed in a region where magnetic field strength is 0.5 T. The torsion wire has rigidity 3×10–6 Nm/ ºC. Determine
(a) Current sensitivity of the galvanometer.
(b) The maximum and minimum torque the coil experiences, if current in the coil is 3mA?
(c) Deflection of coil if 3mA current passes through it?
A nswers
SCREENING EXAMINATION
1. (A) 2. (D) 3. (A) 4. (B) 5. (C 6. (B) 7. (B)
8. (D) 9. (B) 10. (D) 11. (A 12. (C) 13. (A) 14. (D)
15. (B) 16. (D) 17. (D) 18. (C) 19. (D) 20. (A 21. (A)
22.
(C)
23.
(D)
24.
(B)
25.
(D)
26.
(D)
27.
(D)
28.
(C)
MAIN EXAMINATION
1. V0 =
900
13
m / s
f = 3.25 Hz 2. 4710 mm3 3. H =
32L2
2g
4. i > 45º 5. =
9 mV
4ML
6. V =
3Kq (6r2t)1/ 3
VR
7. VD =
3 8. A = 2
2 5
9. =
1
2 tan
h
10. =
11.
1 3 9
9 : 7 : 1
12. = 5
2
RC.
13. (a)ZA = 41; ZB = 31 (b)
A 16
B = 9
14. H =
2 A2
2g
+ 2A ; V = 5A2 2
15. =
u0 nb2I0 sint 2R
16. T = 8.33ºC ; W = 3 × 10–4 J
17. (a) 150º (b) 60º, 60º 18. (a) 3º /mA ; (b) 2.7 × 10–5 Nm, O ; (c) 9º
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