Topic : 07 [Center of Mass]
Click Here
Click Here
1.
A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the
circumferences of the discs coincide. The centre of mass of the new disc is αR distance from the
centre of the bigger disc. The value of α is:
(A) 1/3
(B) 1/2
(C) 1/6
(D) ¼
For Solution – Click Here
2.
A thin rod of length 'L' is lying along the x -axis with its ends at x = 0 and x = L. Its linear density
x n
(mass/length) varies with x as k (L) , where n can be zero or any positive number. If the position
xCM of the centre of mass of the rod is plotted against 'n', which of the following graphs best
approximates the dependence of xCM on n ?
(A)
(B)
(C)
(D)
For Solution – Click Here
3.
Distance of the centre of mass of a solid uniform cone from its vertex is z0 . If the radius of its
base is R and its height is h then z0 is equal to
h2
(A) 4R
3h
(B) 4
5h
(C) 8
3h2
(D) 8R
For Solution – Click Here
4.
Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right
angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of
the system is at a point :
(A) 0.6 cm right and 2.0 cm above 1kg mass
(B) 2.0 cm right and 0.9 cm above 1 kg mass
(C) 0.9 cm right and 2.0 cm above 1kg mass
(D) 1.5 cm right and 1.2 cm above 1kg mass
For Solution – Click Here
5.
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4 kg.
(The coordinates of the same are shown in figure) are:
(A) (1.25 m, 1.50 m)
(B) (0.75 m, 0.75 m)
(C) (0.75 m, 1.75 m)
(D) (1 m, 1.75 m)
For Solution – Click Here
2|Page
6.
As shown in figure. When a spherical cavity (centred at O) of radius 1 is cut out of a uniform
sphere of radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at
G, i.e on the surface of the cavity. R can be determined by the equation:
(A) (R2 – R + 1) (2 – R) = 1
(B) (R2 + R+ 1) (2–R) = 1
(C) (R2 – R – 1) (2 – R) = 1
(D) (R2 + R – 1) (2 – R) = 1
For Solution – Click Here
7.
A rod of length L has non-uniform linear mass density given by ρ(x) = a + b (L) , where a and
X 2
b are constants and 0 ≤ x ≤ L. The value of x for the centre of mass of the rod is at:
4
a+b
(A) 3 (2a+3b) L
3 2a+b
(B) 4 (3a+b) L
3 2a+b
(C) 2 (3a+b) L
3
a+b
(D) 2 (2a+b) L
For Solution – Click Here
8.
Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates
(0,0)cm and (x, 0)cm respectively. The block of 10 kg is moved on the same line through a
distance of 6 cm towards the other block. The distance through which the block of 30 kg must
be moved to keep the position of centre of mass of the system unchanged is :
(A) 4 cm towards the 10 kg block (B) 2 cm away from the 10 kg block
(C) 2 cm towards the 10 kg block (D) 4 cm away from the 10 kg block
For Solution – Click Here
9.
A body of mass M at rest explodes into three pieces, in the ratio of masses 1: 1: 2. Two smaller
pieces fly off perpendicular to each other with velocities of 30 ms −1 and 40 ms −1 respectively.
The velocity of the third piece will be :
(A) 15 ms −1
(B) 25 ms −1
(C) 35 ms −1
(D) 50 ms −1
For Solution – Click Here
10. The identical spheres each of mass 2M are placed at the corners of a right angled triangle with
mutually perpendicular sides equal to 4 m each. Taking point of intersection of these two sides
as origin, the magnitude of position vector of the centre of mass of the system is
4√2
x
, where the
value of x is _____.
For Solution – Click Here
11. What percentage of kinetic energy of a moving particle is transferred to a stationary particle
when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on
elastic collision)
(A) 50.0%
(B) 66.6%
(C) 55.5%
(D) 33.3%
3|Page
For Solution – Click Here
12. As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball
Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the
collision to be elastic, the velocity of ball Q after collision will be : (g = 10 m/s 2 )
0.25 m
(A) 0
(B)
(C) 2 m/s
For Solution – Click Here
(D) 4 m/s
s
13. A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in
horizontal direction, hits the centre of the ball. After collision both travels independently. The
ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from the foot of the
post. The value of initial velocity of the bullet will be (if g = 10 m/s 2 ) :
(A) 120 m/s
(B) 60 m/s
(C) 400 m/s
(D) 360 m/s
For Solution – Click Here
14. A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a
speed of 100 m s −1 each. The recoil velocity of the gun is :
(A) 0.02 m/s
(B) 2.5 m/s
(C) 1.5 m/s
(D) 0.6 m/s
For Solution – Click Here
15. Figures (a),(b),(c) and (d) show variation of force with time.
The impulse is highest in figure.
(A) Fig (c)
(B) Fig (b)
For Solution – Click Here
(C) Fig (a)
(D) Fig (d)
16. A ball is dropped from a height of 20 m. If the coefficient of restitution for the collision
between ball and floor is 0.5, after hitting the floor, the ball rebounds to a height of ______ m.
For Solution – Click Here
17. A man of 60 kg is running on the road and suddenly jumps into a stationary trolley car of mass
120 kg. Then. the trolley car starts moving with velocity 2 ms −1 . The velocity of the running
man was _____ ms −1 . when he jumps into the car.
4|Page
For Solution – Click Here
18. A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired
towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v/3
and the bob just completes the vertical circle. The value of v is _____ ms −1 (if g = 10 m/s 2 )
For Solution – Click Here
19. A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After
collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s.
The initial speed of the smaller body before collision is _____ ms −1.
For Solution – Click Here
20. A body starts falling freely from height H hits an inclined plane in its path at height h. As a
result of this perfectly elastic impact, the direction of the velocity of the body becomes
H
horizontal. The value of h for which the body will take the maximum time to reach the ground is
______.
For Solution – Click Here
Join Telegram Group : Click Here
Download App : Click Here
ANSWER KEY
Ques.
1
8
15
Ans
A
C
B
Ques.
2
9
16
Ans
D
B
5
Ques.
3
10
17
Ans
B
3
6
Ques.
4
11
18
Ans
C
C
10
Ques.
5
12
19
Ans
C
C
4
Ques.
6
13
20
Ans
B
D
2
Ques.
7
14
Ans
B
D
5|Page