CLASS TEST
CLASS
TEST
PHYSICS
CLASS TEST # 37
SECTION-I
Single Correct Answer Type
1.
5 Q. [3 M (–1)]
In the shown diagram a cannon attached to a moving wedge having total mass (cannon + wedge + bullet
= 3m) as shown in figure. Initially system is at rest. Cannon release bullet of mass 'm' with speed u 'w.r.t'
wedge. Find out maximum compression in spring in subsequent motion (Collision between wedge and
block is perfectly elastic and initially spring is in natural length). Assume all surface are frictionless :u
q
k
3R
2m u cos q
k
3
(A)
2.
(B)
2m
2m
2R
m u cos q
k
3
2m u sin q
k
3
(C)
(D)
m u sin q
k
3
A ball of mass 'm' is moving with initial velocity 4iˆ m/sec. It strikes a fixed incline plane such that angle
of incidence of the ball with normal = angle of reflection of ball with normal. Velocity vector of ball just
after collision will be :- (No friction is present between surfaces of ball and wedge)
Normal
4 ^i m/s
m
fixed
q = 30
(
)
(A) ˆi + 3jˆ m / s
3.
(B)
(
(
)
1 ˆ
i + 3jˆ m / s
2
)
(
(C) 2 iˆ + 3jˆ m / s
)
(D) 4 iˆ + 3jˆ m / s
A bullet of mass m is shot with a velocity u at an angle q = 60° with the horizontal which strikes the box
of mass 2m resting at the edge of a smooth surface 'OB' as shown in figure. Bullet strikes the box
horizontally. After that bullet passes through the box and moves with velocity u/4 along horizontal
direction. If bullet rebound elastically with wall AB. Then find the final position where bullet again
strikes mass 2m.
/////////////////////////////
y
2m
(0,0)
u
m
q = 60°
(B)
L
,0
3
u/4
m
///////////////////////////////////////
//////////////////////////////
O
L
A
Elastic wall
B
x
///////////////////////////////////////////////////////
(A)
L
,0
2
PHYSICS / Class Test # 37
(C)
2L
,0
3
(D)
L
,0
4
E-1/5
4.
Two smooth sphere made of identical material having masses m and 2m undergo an oblique impact as
shown in figure. The coefficient of restitution
y
v = 10m/s
2m
f
5
. The velocity of the mass 2m after collision will be :9
f=sin (4/5)
–1
x
m
v=5m/s
(A) 5.
10 ˆ ˆ
i -8j
3
5
(B) - iˆ + 4ˆj
3
5
(C) + ˆi + 4ˆj
3
10 ˆ ˆ
i -8j
3
Two bodies of masses M and m (M > m) are attached to the two ends of a light inextensible string
passing over a frictionless pulley. The system is held at rest with the string taut and vertical with both
masses at a height 'd' above an inelastic table. The system is now released. Calculate the height to which
the larger mass will rise after it has hit the table.
æ m ö
÷d
èM+mø
(A) ç
æ
æ m ö
÷d
è M-mø
m2
ö
(C) ç M2 + m2 ÷ d
(B) ç
è
Multiple Correct Answer Type
6.
(D)
ø
2
æ m ö
÷ d
èM+mø
(D) ç
7 Q. [4 M (–1)]
A ball is dropped as shown in figure. Both the inclined planes are smooth and ball makes perfect
inelastic collision with both planes
(A) maximum height of ball on second plane is
5
h
16
5
(B) maximum height of ball on second plane is h
4
h
h
30°
30°
(C) Total impulse on ball from start to maximum height on second plane is zero.
(D) Total distance covered by ball from start to maximum height on second plane is
7.
29
h
8
A smooth uniform square wall frame of mass m of edge length 2a and small height lies in a smooth
horizontal plane. At t = 0 a particle of mass m hits with speed v 2 , one of the inner wall of the frame
horizontally at an angle 45° from wall normal. Collision is perfectly elastic. The initial collision takes
place at the mid point of wall A.
A
(A) Next collision takes place when t =
a
.
v
3a
(B) KE of frame when t =
, is mv2
2v
(C) after collision at B next collision takes place at wall D
(D) particle and frame comes to rest at regular intervals of time
E-2/5
B
D
C
PHYSICS / Class Test # 37
8.
9.
10.
11.
The figure shows the velocity as a function of time for an object with
mass 10 kg being pushed along a frictionless surface by external force.
At t = 3s, the force stops pushing and the object moves freely. It then
collides head-on and sticks to another object of mass 25 kg.
(A) External force acting on the system is 50 N.
(B) Velocity of the second particle just before the collision is 1 ms–1.
(C) Before collision both bodies are moving in the same direction.
(D) Before collision, bodies are moving in opposite direction.
In an elastic collision between spheres A and B of equal mass but unequal radii, A moves along the
x-axis and B is stationary before impact. Which of the following is possible after impact?
(A) A comes to rest
(B) the velocity of B relative to A remains the same in magnitude but reverses in direction
(C) A and B move with equal speeds, making an angle of 45° each with the x-axis.
(D) A and B move with unequal speeds, making angles of 30° and 60° with the x-axis respectively.
A molecule capable of vibrations is modeled as two point atoms of mass M connected by a spring.
Initially molecule is not vibrating when it collides elastically with a single atom of mass M as
shown in figure. Mark the CORRECT option (s) :2v 0 atom M
(A) Velocity of centre of mass of system consisting of atom and molecules is
.
3
M
Mv 20
(B) Maximum energy stored in spring is
.
v
0
4
molecule
v0
(C) Velocity of centre of mass of molecule after collision is
.
M
2
(D)Momentum of molecule after collision is Mv0.
Two masses (m < M) are released from rest inside a smooth fixed hemispherical bowl. They collide
at the bottommost point.
m
M
R
2
3M - m ö
(A) If the collision is elastic, the smaller mass m reaches maximum height of R æç
÷ from
è m+M ø
bottom.
2
æ M - 3m ö
(B) If the collision is elastic, the larger mass M reaches a maximum height of R ç
÷ from
è m+M ø
bottom.
2
æ 2M - m ö
(C) If the collision is elastic, the smaller mass m reaches maximum height of R ç
÷ from
è m+M ø
bottom.
2
æ 2M - m ö
(D) If the collision is elastic, the larger mass M reaches maximum height of R ç
÷ from
è m+M ø
bottom.
PHYSICS / Class Test # 37
E-3/5
12.
Two balls of mass m each are connected by a weightless spring (figure) of force constant k and
length of L and lie motionlessly on a smooth horizontal table. The third ball of mass m moves with
speed of v0 on the line connecting the centers of first two, and elastically collides with one of them.
Assuming that time of impact of balls is very small in comparison to time of spring deformation :L
v0
m
m
m
(A) The maximum distance between the first two balls during their further movement
L max = L + v o
m
.
(2k)
(B) The third ball comes to rest
(C) The maximum distance between the first two balls during their further movement
L max = L + v o
m
.
(k)
(D) The minimum distance between the first two balls during their further movement
L min = L - v o
m
(2k)
Linked Comprehension Type
(Single Correct Answer Type)
(1 Para × 3Q.)
[3 M (-1)]
Paragraph for Question 13 to 15
Meson is composed of two quarks and the interaction between the quarks is complicated. Research
of meson can be done by studying the inelastic collisions between the meson and high energy
electrons. As the collision is quite complicated, scientists invented a simplified model called “parton
model” to grasp the main content during collision. In the model, the electron first collides with part
of meson (e.g. one of the quarks) elastically. Then the energy and momentum are transferred to the
other quark and thus the whole meson during subsequent interaction. This simplified model is
described by the following:
Electron
Meson
13.
An electron of mass M and energy E collides with a quark of mass m1 in a meson. The other quark in
the meson has mass m2. The quarks are connected by a massless spring of natural length L which is
at equilibrium before collision. All movements are on a straight line and neglect the effect of
relativity. Find, after collision,
The energy gain of the quark m1
4Mm1
(A) ( M + m )2 E
1
14.
2Mm1
(B) ( M + m )2 E
1
Mm1
3Mm1
(C) ( M + m )2 E
(D) 2 ( M + m )2 E
1
1
The minimum kinetic energy of the meson as a whole system
4Mm12
(A) M + m 2 m + m
(
1) (
1
2)
2Mm12
(C) M + m 2 m + m
(
2) (
1
2)
E-4/5
E
E
4Mm12
(B) M + m 2 m + m E
(
2) (
1
2)
2Mm12
(D) 3 M + m 2 m + m E
(
2
) ( 1
2
)
PHYSICS / Class Test # 37
15.
The internal energy of the meson which is expressed by the oscillation of the spring.
4Mm1 m2
4Mm1 m2
(A) ( M + m )2 ( m + m ) E
1
1
(B) ( M + m )2 ( m + m ) E
2
2
2Mm1 m2
1
(D) ( M + m )2 ( m + m ) E
2
2
1
SECTION-III
Numerical Grid Type (Single digit Ranging from 0 to 9)
1.
2
3 Q. [4 M(0)]
The centres of the spheres 1, 2 and 3 lie on a single straight line. Sphere 1 is moving with an (initial)
velocity v1 directed along this line and hits sphere 2. Sphere 2, acquiring after collision a velocity v2, hits
sphere 3. Both collisions are absolutely elastic. What must be the mass of sphere 2 (in kg) for the sphere
3 to acquire maximum velocity (The masses m1 and m3 of spheres 1 and 3 are 9kg & 1kg respectively)?
1
m1
2.
2
3Mm1 m2
(C) ( M + m )2 ( m + m ) E
2
1
v1
2
m2
3
m3
Initially there is a small ball moving with speed 2v towards wall A and both walls are moving with
constant velocity towards each other as shown in figure. Then find speed v (in m/s) if time taken by the
ball in first three collision is 5 sec. (Assume all collision are perfectly elastic and friction is absent).
A
B
105m
v
v
2v
3.
In the arrangement shown, the pendulum A is pulled aside. It is then released and allowed to collide
with other pendulum B which is at rest. A perfectly inelastic collision occurs and the system rises to a
height
mA
1
h. The ratio of the masses of the pendulums m is
4
B
h
PHYSICS / Class Test # 37
E-5/5
CLASS TEST # 37
ANSWER KEY
SECTION-I
Single Correct Answer Type
1. Ans. (A)
5. Ans. (D)
2. Ans. (C)
5 Q. [3 M (–1)]
3. Ans. (C)
4. Ans. (B)
8. Ans. (A, B, C)
12. Ans. (A,B,D)
9. Ans. (A,B, C, D)
Multiple Correct Answer Type
6. Ans. (A,C,D)
10. Ans. (A,B,C,D)
7. Ans. (A,B,D)
11. Ans. (A, B)
7 Q. [4 M (–1)]
Linked Comprehension Type
(Single Correct Answer Type)
13. Ans. (A)
14. Ans. (A)
(1 Para × 3Q.)
15. Ans. (A)
SECTION-III
Numerical Grid Type (Single digit Ranging from 0 to 9)
1. Ans. 3
2. Ans. 9
[3 M (-1)]
3. Ans. 1
3 Q. [4 M(0)]