Physics test2011 1

IITGuide.com - PAPER -1 - Duration 60 Minutes 1

No. of
Question Type Marking Scheme Maximum marks
Questions
8 Single Answer Type 3 marks for correct answer; −1 for wrong 24
4 Multiple Answer Type 4 marks for correct answer; −1 for wrong 16
6 Comprehension Type 4 marks for correct answer; −1 for wrong 24
2 marks for each correct answer; No negative
2 Matrix-Matches 16
marking
Total = 20 Total = 80

SECTION – I
This section contains 8 multiple choice questions. Each question has 4 choices (a), (b), (c) and
(d) for its answer, out of which ONLY ONE is correct.

1. A charge q is placed at some distance along the axis of a uniformly charged disc of surface
charge density σ. The flux due to the charge q through the disc is φ. The electric force on
charge q exerted by the disc is
σφ σφ σφ
(a) σφ (b) (c) (d)
4π 2π 3π
2. Find the reading of the ideal ammeter connected in the 10V 4V 8V 6V
given circuit. Assume that the cells have negligible
internal resistance.
(a) 0.8 A 10Ω 8Ω 4Ω 2Ω A
(b) 0.25 A
(c) 1.95 A
(d) 1.0 A
3. A ray of light strikes a horizontal plane mirror at an angle of 45°. A second plane mirror in
attached at an angle θ with it. If ray after reflection from second mirror runs parallel to the
first mirror, then θ is
(a) 45° (b) 60° (c) 67.5° (d) 135°
4. The moment of inertia of a cube of mass m and side ‘a’ about one of its edges is equal to
2 4 8
(a) ma 2 (b) ma 2 (c) 3ma 2 (d) ma 2
3 3 3
1
5. The diagram shows the variation of
1
(where v is velocity of the ( m s )-1
v
v
particle) with respect to time. At time t = 3 s using the details
1
given in the graph, the instantaneous acceleration will be equal to 3 45°
(a) −2 m s 2 (b) +3m s 2
t(s)
(c) +5m s 2 (d) −6 m s 2 3s

6. A container has two immiscible liquids of densities ρ1 and
ρ 2 ( > ρ1 ) . A capillary tube of radius r is inserted in the liquid so
h ρ1
that its bottom reaches upto the denser liquid. The denser liquid
rises in the capillary and attains a height h from the interface of the
ρ2
liquids, which is equal to the column length of the lighter liquid.
Assuming angle of contact to be zero, the surface tension of
heavier liquid is :
ρ rgh r
(a) 2π r ρ 2 gh (b) 2 (c) ( ρ 2 − ρ1 ) gh (d) 2π r ( ρ 2 − ρ1 ) gh
2 2
7. If the system is released from rest, then match the column:


(i) acceleration of 2 kg mass (a) 2 SI unit
(ii) acceleration of 3 kg mass (b) 5 SI unit
(iii) tension in the string connecting 2 kg mass (c) zero 2kg
(iv) frictional force on 2 kg mass (d)none of these µ=√3/2
30° 3kg

(a) (i) c (ii) b (iii) d (iv) a (b) (i) c (ii) a (iii) b (iv) d
(c) (i) c (ii) c (iii) d (iv) b (d) (i) c (ii) c (iii) d (iv) d
8. What is the largest mass of C in kg that can be suspended without A
moving blocks A and B. The static coefficient of friction for all B
plane surface of contact is 0.3. Mass of block A is 50kg and block B
is 70kg. Neglect friction in the pulleys:
C
(a) 120 kg (b) 92 kg
(c) 81 kg (d) None of these
SECTION – II
This section contains 4 multiple type questions. Each Question has 4 choices (a), (b), (c) and
(d), for its answer, out of which ONE OR MORE is/are correct.

9. A uniform rod AB of length 7m is undergoing combined 11m/s A
rotational and translational motion such that, at some instant of
time, velocities of its end points A and centre C are both
perpendicular to the rod and opposite in direction, having C 3m/s
magnitudes 11 m/s and 3 m/s respectively as shown in the figure.
Velocity of centre C and angular velocity of the rod remains
constant.
(a) acceleration of point A is 56 m/s2 B
2
(b) acceleration of point B is 56 m/s
(c) at the instant shown in the figure acceleration of point B is more than that of point A.
(d) angular velocity of the rod is 4 rad/sec
10. The temperature change versus heat supplied curve is given for Temperature
C
(K) D
1 kg of a solid block. Then, which of the following statements
A B
is/are correct? 60°
(a) Specific heat capacity of the solid is 1 J/kg K. 45°
(b) Specific heat capacity of liquid phase is 3 J/kg K. 0
100 J 200J
(c) Latent heat of vaporization is 100 J/kg Heat supplied (J)

(d) Latent heat of vaporization is 200 J/kg.
11. Three capacitors each having capacitance C = 2µF are connected S
with a battery of emf 30 V as shown in the figure. When the switch S
is closed, then C
(a) the amount of charge flown through the battery is 20 µC C
(b) the heat generated in the circuit is 0.6 mJ C
(c) the energy supplied by the battery is 0.6 mJ
30V
(d) the amount of charge flown through the switch S is 60 µC
12. A uniform rod of mass m = 2 kg and length l = 0.5 m is sliding along two mutually
perpendicular smooth walls with the two ends P and Q having velocities
vP = 4m s and vQ =3m s as shown. Then:
(a) The angular velocity of rod, ω =10 rad/s, counter clokwise .


(b) The angular velocity of rod ω = 5.0 rad/s. counter clockwise Q

(c) The velocity of center of mass of rod, v cm =2.5 m s .
vQ=3m/s
25
(d) The total kinetic energy of rod, K = joule. P
3 vP=4m/s

SECTION – III
This section contains 3 groups of questions. Each group has 2 multiple choice questions based
on a paragraph. Each question has 4 choices (a), (b), (c) and (d), for its answer, out of which
ONLY ONE is correct
PASSAGE I : Q13 to Q14
Two uniform rods AB and BC of masses 1kg and 2kg having lengths A
2m and 1m respectively are joined to each other at B. The assembly is 2m
kept on a smooth horizontal surface as shown in figure. A horizontal
P
impulse P = 10 N-s is applied on the rod AB at a distance 0.5 m from
point B perpendicular to the rod. 0.5m
B
1m
C
13. Velocity of centre of rod AB just after the application of impulse is
25 35 25
(a) m/s (b) m/s (c) m/s (d) 6 m/s
12 6 2
14. Impulse applied by the rod BC on the rod AB during application of impulse P is
25
(a) 25 N-s (b) 10 N-s (c) N-s (d) 12.5 N-s
6
PASSAGE II : Q15 to Q16 :
S
C1
In the circuit shown in figure, E1 = E2 = 100 volt,
+ +
R1 = R2 = 4Ω , C1 = 6µF and C2 = 3µF. When switch S is C2 _ E2
_ E1
closed and electrical equilibrium is attained.
R1 R2

15. Energy drawn from battery E1 after closing the switch is :
(a) 0.03 J (b) 0.02 J (c) –0.03J (d) –0.02 J
16. Heat generated in the circuit is :
(a) 0.003 J (b) 0.002 J (c) 0.005J (d) 0.006 J
PASSAGE III : Q17 to Q18 :
S1
The capacitor C1 in the figure shown initially carries a charge q0 . When
+q R
the switches S1 and S2 are closed, capacitor C1 is connected in series to a C1
−
0

resistor R and a second capacitor C2 , which is initially uncharged. C2

S2
17. Find the charge flown through wires as a function of time.
C qo C C −t C R
(a) qo e−t / RC +
qo (b) × ⎡1 − e−t RC ⎤ (c) qo e (d) qo e − t RC
C2 C1 ⎣ ⎦ C1
CC
where C = 1 2
C1 + C2

18. Find the total heat dissipated in the circuit during the discharging process of C1 .
q0 2 qo 2 q 2 o C2 qo 2
(a) ×C (b) (c) (d)
2C12 2C 2C12 2C1C2
SECTION – IV


This section contains 2 questions. Each question contains statements given in two columns
which have to be matched. The statements in column – I are labeled (A), (B), (C) and (D), while
the statements in Column-II are labeled p, q, r, and s. Any given statement in column – I can
have correct matching with ONE OR MORE statement(s) in Column – II. The appropriate
bubbles corresponding to the answers to these questions have to be darkened as illustrated
in the following example.
If the correct matches are A-p, s; B-q and r; C-p and q; and D-s; then the correct darkening of
bubbles will look like the following

p q r s
A p s

B q r

C p q

D s

19. In the given figure, coefficient of friction between the 2kg and F1
2kg rough
3kg blocks are µ S = 0.3 and µ K = 0.2 , between the 5kg and F2
3kg 5kg rough
ground are µ S = µ K = 0.1 and between 3kg and ground are
µS = µ K = 0 , (g = 10 m/s2).
COLUMN – I COLUMN − II
(A) For F1 = 0, F2 = 15 N (p) Acceleration of all blocks will be same
(B) For F1 = 6.25 N , F2 = 0 (q) Acceleration of 2kg and 3kg blocks will be different
Frictional force between 2kg and 3kg block is less than
(C) For F1 = 8 N , F2 = 10 N (r)
maximum static friction
(D) For F1 = 16 N , F2 = 9 N (s) Contact force between 3kg and 5kg block is less than 10 N.
r r ur
20. In circular motion suppose a is the acceleration of particle, v its linear velocity and w its
angular velocity. Then match the following column :
Column – I Column – II
r r
(A) a×v (p) positive
r r
(B) a⋅v (q) negative
ur r
(C) w⋅v (r) Zero
u r
r
(D) w× a (s) undefined

IITGuide.com - PAPER -2 Duration 60 Minutes 1

No. of
Question Type Marking Scheme Maximum Marks
Questions
4 Single Answer Type 3 marks for correct answer; −1 for wrong 12
5 Multiple Answer Type 4 marks for correct answer; −1 for wrong 20
2 marks for each correct answer; No negative
2 Matrix-Matches 16
marking
Single Digit Integer
8 4 marks for correct answer; −1 for wrong 32
Answer Type
Total = 19 Total = 80

SECTION – I
This section contains 4 multiple choice questions. Each question has 4 choices (a), (b), (c) and
(d) for its answer, out of which ONLY ONE is correct.

1. A ball is thrown from the ground to clear a wall 3 m high at a distance of 6 m and falls 18 m
away from the wall, the angle of projection of ball is :
⎛3⎞ ⎛2⎞ ⎛1⎞ ⎛3⎞
(a) tan −1 ⎜ ⎟ (b) tan −1 ⎜ ⎟ (c) tan −1 ⎜ ⎟ (d) tan −1 ⎜ ⎟
⎝2⎠ ⎝3⎠ ⎝2⎠ ⎝4⎠
2. A ball leaves a horizontal table with velocity v0 = 5 m/s . The ball v0=5m/s

bounces elastically from a vertical wall at a horizontal distance D
(= 8m) from the table, as shown in figure. The ball then strikes h=20m
the floor a distance x0 from the table (g = 10 m/s2). The value of
x0 is
x0
(a) 6 m (b) 4 m D
(c) 5 m (d) 7 m
[

3. In the given circuit diagram, find the heat generated on closing C 2C
the switch S. (initially the capacitor of capacitance C is
uncharged)
3C
3 S V
(a) CV 2 (b) CV 2
2
1
(c) CV 2 (d) none of these
2
i1 i2 2Ω 4Ω 3Ω
4. In the circuit shown in figure the ratio of currents is
(a) 2 2Ω 8Ω 1Ω
(b) 8 16V
(c) 0.5 8Ω
i2
8Ω i1
(d) 4
8V
SECTION – II
This section contains 5 multiple type questions. Each Question has 4 choices (a), (b), (c) and
(d), for its answer, out of which ONE OR MORE is/are correct.

5. Coefficient of friction between the two blocks is 0.3 whereas 2kg T1
the surface AB is smooth. (g = 10 m/s2)
(a) Acceleration of the system of masses is 5.86 ms−2 T2 3kg
(b) Tension T1 in the string is 17.7 N A B
(c) Tension T2 in the string is about 41.4 N 10kg
(d) Acceleration of 10 kg mass is 7.55 ms−2


6. In the circuit shown in figure, R1 = R2 = R3 = R . Switch is closed at R1

time t = 0 . Then, C
V
(a) potential difference across R2 is equal to potential difference R3
S R2
across R3 at t = ⎛
CR ⎞
⎜ ⎟ ln ( 2 )
⎝ 2 ⎠
V
(b) maximum current through R3 is
2R
V
(c) minimum current through R3 is
2R
V
(d) maximum charge stored in the capacitor is C
2
7. A force F is applied on a block of mass 2 kg as shown in figure. F

( )
g = 10m s 2 . 2Kg

(a) The force of friction when the block is moving is 8N. µs = 0.6
µk = 0.4
(b) The force of friction when the block is stationary is less than 12 N.
(c) Block will not leave contact with ground for any value of F.
(d) The force of friction when the block is moving is less than 8 N.
8. A variable voltage V = 2 t is applied across an inductor of inductance L = 2 H as shown in
figure. Then
(a) current versus time graph is a parabola 2H
(b) energy stored in magnetic field at t = 2 sec is 4 J V = 2t
(c) potential energy at time t = 1 sec in magnetic field is increasing at a rate of 1 J/s
(d) energy stored in magnetic field is zero all the time.

9. A cylinder of radius R is to roll without slipping between two planks as V

shown in the figure. Then:
v
(a) angular velocity of the cylinder is counter clockwise
R 3V
2v
(b) angular velocity of the cylinder is clockwise
R
(c) velocity of centre of mass of the cylinder is v towards left
(d) velocity of centre of mass of the cylinder is 2v towards right

SECTION – III
This section contains 2 questions. Each question contains statements given in two columns
which have to be matched. The statements in column – I are labeled (A), (B), (C) and (D), while
the statements in Column-II are labeled p, q, r, and s. Any given statement in column – I can
have correct matching with ONE OR MORE statement(s) in Column – II. The appropriate
bubbles corresponding to the answers to these questions have to be darkened as illustrated
in the following example.
If the correct matches are A-p, s; B-q and r; C-p and q; and D-s; then the correct darkening of
bubbles will look like the following

P q r s
A p s

B q r

C p q

D s


10. A block of mass 1 kg is placed on a rough horizontal surface of coefficient of friction µ = 0.2.
A force is applied on the block horizontally whose variation with time is shown in the figure.
F(N)
1Kg F
8
µ =0.2
2
1 t(s)
1 2 8 30
COLUMN – I COLUMN − II
(A) Velocity of particle is zero at (p) t = 1 s
(B) Acceleration of particle is non-zero at (q) t = 4 s
(C) Friction force = 1 N (r) t = 20 s
(D) Friction force ≥ F (s) t = 30 s
11. The equivalent capacitance across AB for the plates connected as shown in column I, are
given in column II. Match the items in column II with the items in column I. Area of each
plate is A unless mentioned.
Column –I Column II
A 3ε0 A
(p)
d 4d
2d
3d

(A) B

2ε0 A
d A
(q)
d 3d
B
(B)

A
ε0 A
d (r)
d 4d
B
(C) d

A

ε0 A
d (s)
2d A/2 2d
A/2
(D) B

SECTION – IV
This section contains 8 questions. The answer to each of the questions is a single-digit integer,
ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the
ORS have to be darkened. For example, if the correct answers to question numbers X, Y, Z
and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like
the following

X Y Z W
0 0 0 0
1 1 1 1
2 2 2 2


3 3 3 3

4 4 4 4
5 5 5 5
6 6 6 6

7 7 7 7
8 8 8 8

9 9 9 9

12. Find the natural frequency (in Hz) of the system as shown in the figure. The k
pulleys are massless and frictionless.

( )N
Take : k = π 2
m
and m = 1 kg m

13. A ring rolls on a horizontal surface without sliding. The velocity of the centre is v. It
encounters a step of height 0.3 R where R is the radius of the ring. Calculate the angular
velocity (in radian/second) of the ring just after the impact. Assume that the ring does not
return back. (and there is sufficient friction to avoid slipping).
m
Take : V = 6 and R = 1.7 m
s

14. The four terminal network shown in the figure consists of four A

equal resistors and is a part of a larger circuit. The points A, B r
r
r
and C are at same potential. The potential difference between A O
B D
and D is 4 volts. Find potential difference (in Volts) between O r
and D. C

1 A
15. The pressure and volume of an ideal gas are related as P ∝ 2
for a 3P0
V
process A → C as shown in the figure. The pressure and volume at A
C
is 3P0 and V0 respectively and the pressure at C is P0 . Find the work P0

done (in J) in the process A → C
( )
V0
Given that : PV0 = 3 + 3 J
0

16. A source S having a detector D moving towards a wall with a certain velocity
detects 9 beats per second. On doubling the velocity of the source, the detector D
205
detects 20 beats per second. The original frequency of sound source is . Find S
x
value of x. Take speed of sound as 330 m/s.

17. A ball is projected normally from point P (which is on an inclined plane) with 90°
Q

speed u. It strikes the vertical wall normally. If all the collisions are perfectly P 90°

elastic, then find the time period (in seconds) of periodic motion. 45°
m m
Given : u = 10 2 , g = 10 2
s s


g
18. The magnitude of acceleration of M is . Find the value of x. Given that
x
M
= 2. M
m m

19. The block of mass ‘m’ initially at x = 0 is acted upon by a
horizontal force F = a − bx as shown in the figure. The coefficient
F
of friction between the surfaces of contact is µ. The net work done
x=0
on the block is zero. The distance traveled by the block before x
stopping is x/5 m. Find value of x.
m
Take : a=1N,b=1N/m,µ = 0.3, g = 10 2 and m = 0.1 Kg
s

Physics test2011 1

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