The center of mass of a system of particles does not depend upon,

(a)

position of particles

(b)

relative distance between particles

(c)

masses of particles

(d)

force acting on particle

A couple produces,

(a)

pure rotation

(b)

pure translation

(c)

rotation and translation

(d)

no motion

The angular momentum of a rotating body is doubled, its K.E. of rotation becomes ________________

(a)

Two times

(b)

Four times

(c)

Halved

(d)

Eight times

A particle undergoes uniform circular motion. The angular momentum of the particle remain conserved about,

(a)

the center point of the circle

(b)

the point on the circumference of the circle

(c)

any point inside the circle

(d)

any point outside the circle

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

(a)

15MR²/32

(b)

13MR²/32

(c)

11MR²/32

(d)

9MR²/32

The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle \(\theta\) without slipping and slipping down the incline without rolling is,

(a)

5: 7

(b)

2: 3

(c)

2: 5

(d)

7: 5

Where will be the centre of mass on combining two masses m and M (M > m)?

(a)

Towards m

(b)

Towards M

(c)

Between m & M

(d)

away from m & M

Two bodies of masses 2 kg and 3 kg have position vectors \(\hat { i } +2 \hat { j} +\hat { k} \) and \(\hat { -4i } - \hat {(-3j)} +\hat { 6k} \) respectively. The centre of mass of this system has a position vector _____________.

(a)

\(\hat {- 3i } -\hat { j}\)

(b)

\(\hat {5 i } - \hat { j} +2\hat { k} \)

(c)

\(\hat {-2 i } - \hat { j} +4\hat { k} \)

(d)

\(\hat { -3i } - \hat { j} +\hat7 { k} \)

Four identical spheres each of mass m are placed at the corners of square of side 2 m. Taking the point of intersection of the diagonals as the origin the coordinates of the centre of mass are?

(a)

(1, 1)

(b)

(0, 0)

(c)

(1, -1)

(d)

(-1, 1)

Two blocks of masses 20 kg and 5 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of 15 m/s to the heavier block in the direction of lighter block. The velocity of centre of mass is _____________.

(a)

22 ms^-1

(b)

30 ms^-1

(c)

12 ms^-1

(d)

15 ms^-1