TPT-4

PHYSICS
B

Date : Time : 75 Min. Max. Marks : 80

Marking Scheme :

SCQ - 1 - 3, (4, –1)

MCQ = 4 - 9, (4, –1)
Comprehen sion = 10 - 18, (4, –1)
Integer = 19 - 20, (4, –1)

Submit (E) : 18-10-2016 (RKH Sir)

Final (E) : 20-10-2016 (RKH Sir) _Time : 3 : 14 pm

SECTION-1 : (Only One option correct type)

This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and
(D) out of which ONLY ONE is correct.

1. A smooth horizontal disc rotates about the vertical axis O with a constant angular velocity . A thin
uniform rod AB of length  performs small oscillations about the vertical axis A fixed to the disc at a
distance 'a' from the axis of the disc. Find the frequency 0 of these oscillations. Assuming that  << a.
[Irodov book]

3a2 3a 2 2 5a 22 a2

(A) = (B)  = (C)  = (D)  =
2 2 2 2 2 2

2. A cylindrically symmetric body is attached to two identical cords at points near its ends. The cords are
partially wound in the same sense around the cylinder, and their free ends are fastened to points on a
ceiling; initially, the cords are vertical and the cylinder is horizontal. A third cord is attached to and
wound (in the same sense as the other two cords) around the middle of the cylinder; a heavy weight is
tied to the free end of this cord (see figure). (Assuming mass of cylinder and heavy weight are same)
[200 more problems book]

When the system is released from rest, what is the acceleration of the heavy weight?
g 6g 3g
(A) (B) (C) (D) g
2 11 11
3. Find value of R so that rate of heat develop in it will be maximum. (Assuming all battery are ideal)
[Made RKH Sir_2016-17]
R R0 R0

E1 2R0 2R0 E4

R0 E2

E3 R0
(A) 2R0 (B) 3R0
(C) R0 (D) depending on value of emf of battery

SECTION-2 : (One or more option correct type)

This section contains 6 multiple choice question. Each question has four choices (A), (B), (C) and (D)
out of which ONE or MORE are correct.

4. A simple pendulum is released from rest with its string horizontal. Which of the two arcs, AP and PB as
defined in the figure. Which of following options is/are correct ?
[200 more problems book]

A 30°

B

(A) In path AP, bob will take time greater than .
g
(B) In path AP, bob will take more time than that of in path PB.
(C) In path AP, bob will take less time than that of in path PB.
(D) In path AP, bob will take equal time than that of in path PB.

5. A uniform rod of mass m and length L is fitted at each end with a frictionless bearing in the form of a
freely rotating wheel, for which the rod acts as an axle. The two bearings are identical and have
negligible masses compared to that of the rod.
How does the rod move if it is placed on a horizontal rough surface – assuming that the bearings roll on
it without slipping – and the two ends of the rod are initially given parallel velocities of v1 and v2 in a
direction that is perpendicular to the axis of the rod? Assuming V 1 < V2
[200 more problems book]
V2
V1
L

1  V1  V2 
(A) Centre of mass of rod moving on circle of radius R =   L
2  V2 – V1 
 V – V1 
(B) Centre of mass of rod moving on circle of radius R =  2  L
 V1  V2 

 m V22 – V12
(C) Net friction force on system is equal to fr = 
 
 2L 
 

(D) Net friction force on system is equal to fr = 


 m V12  V22  

 L 
 
6. A cone with height h and a base circle of radius r is formed from a sector shaped sheet of paper. The
sheet is of such a size and shape that its two straight edges almost touch on the sloping surface of the
cone. In this state the cone is stress-free. [200 more problems book]

The cone is placed on a horizontal, frictionless table-top, and loaded at its apex with a vertical force of
magnitude w, without collapsing. The splaying of the cone is opposed by a pair of forces of magnitude
F acting tangentially at the join in the base circle (see figure). Ignoring any frictional or bending effects

w  r 
in the paper, if the value of F is   then.
2  h  

(A)  = 1 (B)  = 1 (C)  = 1 (D)  = 2

7. At the top of a long incline that makes an angle with the horizontal, there is a cylindrical vessel
containing water to a depth H. A hole is to be drilled in the wall of the cylinder, so as to produce a water
jet that lands a distance d down the incline. h is made as from the bottom of the vessel should the hole
be drilled in order to make d as large as possible? [200 more problems book]

H
h



1 H
(A) If tan < then maximum value of d is dmax =
2 cos   sin 
1 H
(B) If tan < then maximum value of d is dmax =
2 cos   sin 
1
(C) If tan > then value of h for dmax is 0.
2
1
(D) If tan < then value of h for dmax is 0.
2
8. A time varying magnetic filed produced by solenoid whose centre is same as that of circle in figure. A
very small ring of mass m and charge q is placed on frictionless fixed circular ring as shown in figure. It
initial velocity of ring is zero. [Made RKH Sir_2016-17]
y
× × × × ×
fixed
× × × × × x
m,q
× × × × ×
z
× × × × ×
 B
ˆ
B  0 t( k)
r
where r is distance from centre and B0 is constant
qB0 2qB0
(A) Velocity of ring at time t is t (B) Velocity of ring at time t is t
m m
2qB0
(C) Tangential acceleration of ring at time t is
m
qB0
(D) Tangential acceleration of ring at time t is
m

9. A square loop of side length of  and current carrying  is placed in xy plane as shown in figure. Which
of the following option(s) is/are correct. [Made RKH Sir_2016-17]
y



 x
a

0   a   
(A) The magnetic flux in region x < 0 is n  
2  a 
 0   a   
(B) The magnetic flux in region x < 0 is n  
  a 
0   a   
(C) The magnetic flux in region x < 0 is n  
3  a 
 0   a   
(D) The magnetic flux in region x < 0 is n  
5  a 

SECTION – 3 : (Paragraph Type)

This section contains 3 paragraphs each describing theory, experiment, data etc. Nine questions
relate to three paragraphs. Each question of a paragraph has only one correct answer among the
four choices (A), (B), (C) and (D).
Paragraph for Questions 10 and 12
A small body of mass m tied to a non-stretchable thread moves over a smooth horizontal plane. The
other end of the thread is being drawn into a hole O with a constant velocity. If the thread tension as a
mro o
function of the distance r between the body and the hole is assuming that at r = ro the angular
r
velocity of the thread is equal to 0. [Irodov book]
10. Find value of  :
(A) 3 (B) 2 (C) 4 (D) 1

11. Find value of  :

(A) 3 (B) 2 (C) 4 (D) 1

12. Find value of  :

(A) 3 (B) 2 (C) 4 (D) 1

Paragraph for Question Nos. 13 to 15

–1
Two identical billiard balls of radius 5 cm and each of mass 1Kg, moving with a speed of 3 ms , roll,
without slipping, towards each other on a horizontal rectangular U-shaped trough that is sufficiently
deep that the balls are clear of its base (see figure). The resulting instantaneous collision is perfectly
elastic, and, during it, each ball reverses its linear velocity, though their angular velocities are not
affected. [200 more problems book]

13. How wide does the trough need to be for the balls to collide twice?
(A) 3 cm (B) 5 cm (C) 15 cm (D) 10 cm

14. Angular velocity of ball after collision is (Assuming width of trough is least for second collision)
(A) 30 10 rad / sec (B) 15 10 rad / sec (C) 10 10 rad / sec (D) 60 rad / sec

15. Minimum impulse of friction force so that second collision occure is

(A) 3 Kg m/s (B) 2 Kg m/s (C) 1Kg m/s (D) 10 Kg m/s

Paragraph for Questions 16 and 18

A small smooth pearl of mass 'm' is threaded onto a rigid, smooth, vertical rod, which is pivoted at its
base. Initially, the pearl rests on a small circular disc that is concentric with the rod, and attached to it at
a distance d from the rotational axis. The rod starts executing simple harmonic motion around its
original position with small angular amplitude 0 (see figure). If average normal reaction in in vertical
d  
direction is so that at minimum frequency (), the pearl to leave the rod is 0  m , where C is
C
constant. [200 more problems book]
16. Find value of ?
(A) 2 (B) 3 (C) 4 (D) 5

17. Find value of ?

(A) 4 (B) 3 (C) 2 (D) 1

18. Minimum frequency of oscillation is required for the pearl to leave the rod?
3g 7g 2g 8g
(A) (B) (C) (D)
d20 d20 d02 d02

Integer value correct Type)

This section contains 2 questions. The answer to each question is a single digit integer, ranging from
0 to 9 OR Two digit integer, ranging from 00 to 99 (both inclusive)

19. If shape does an elastic string of mass 'm' take up when its two ends are fixed to points that are at the
m g x 
same height and separated by a moderate distance is y  . Find  ? (Assuming that  is very
2fx dz
small and fx and fy are horizontal and vertical force) [200 more problems book]

d
fy


fx
x
x

+ th nd +3
20. De-excitation energy of He atom from 6 orbit to 2 orbit is used in excite electron of Be atom. Find
+3
initial excited state of Be atom. [Made by RKH Sir 2016-2017]