Systems of Particles and Rotational Motion Test

Result

Systems of Particles and Rotational Motion Test - 41

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Question 1
4 / -1

The centre of mass of a system of two particles divides the distance between them

A
In inverse ratio of square of masses of particles

B
In direct ratio of square of masses of particles

C
In inverse ratio of masses of particles

D
In direct ratio of masses of particles

Solution
Question 2
4 / -1

If linear density of a rod of length 3m varies as λ = 2 + x, then the position of the centre of gravity of the rod is

A

B

C

D

Solution
Question 3
4 / -1

A

B

C

D

Solution
Question 4
4 / -1

A body A of mass M while falling vertically downwards under gravity breaks into two parts a body B of mass 1/3 M and a body C of mass 2/3M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

A
Body C

B
Body B

C
Depends on height of breaking

D
Does not shift
Question 5
4 / -1

Four bodies of equal mass start moving with same speed as shown in the figure. In which of the following combination the centre of mass will remain at origin

A
c and d

B
a and b

C
a and c

D
b and d
Question 6
4 / -1

Three identical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

A

B

C

D

Solution
Question 7
4 / -1

An isolated particle of mass m is moving in a horizontal plane (X–Y) along the X–axis at a certain height above the ground. It suddenly explodes into two fragments of masses m/4 and 3m/4. An instant later, the smaller fragment is at y = 15 cm. The larger fragment of this instant is at

A
y = –5 cm

B
y = +20 cm

C
y = +5 cm

D
y = –20 cm

Solution
Question 8
4 / -1

Centre of mass of 3 particles 10 kg, 20 kg and 30 kg is at (0, 0, 0). Where should a particle of mass 40 kg be placed so that the combination centre of mass will be at (3, 3, 3)?

A
(0, 0, 0)

B
(7.5, 7.5, 7.5)

C
(1, 2, 3)

D
(4, 4, 4)

Solution
Question 9
4 / -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 from the centre of the bigger disc. The value of a is

A
1/3

B
1/2

C
1/6

D
1/4

Solution
Question 10
4 / -1

Two masses m₁ and m₂ (m₁ > m₂) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of centre of mass is

A

B

C

D
Zero

Solution