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

The angular momentum of a system of particles is conserved _____________.

(a)

When no external force acts upon the system

(b)

When no external torque acts upon the system

(c)

When no external impulse acts upon the system

(d)

When axis of rotation remains same

If earth suddenly contracts to 0.75 times of its present radius, then the length of the day becomes _______________

(a)

12 hr

(b)

18 hr

(c)

15.5 hr

(d)

13.5 hr

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

(a)

zero

(b)

 increasing with x

(c)

decreasing with x

(d)

remaining constant

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 speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is,

(a)

\( \sqrt \frac{4}{3}gh\)

(b)

\( \sqrt \frac{10}{7}gh\)

(c)

\(\sqrt{2gh}\)

(d)

\( \sqrt \frac{1}{2}gh\)

A round object of mass M and radius R rolls down without slipping along an inclined plane. The fractional force, 

(a)

dissipates kinetic energy as heat

(b)

decreases the rotational motion

(c)

decreases the rotational and transnational motion

(d)

converts transnational energy into rotational energy

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 objects which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are 4v and 2v at any instant, then the speed of centre of mass of the system will be ________________.

(a)

2v

(b)

zero

(c)

V

(d)

1.5 v

If I, \(\alpha \) and \(\tau \) are MI, angular acceleration and torque respectively of a body rotating about any axis with angular velocity \(\omega \), then _____________.

(a)

\(\tau =I\omega \)

(b)

\(\tau =I\alpha \)

(c)

\(\alpha =r\omega \)

(d)

\(\alpha =r\omega \)

Consider a system of two identical particles. One is at rest and the other has an acceleration \(\overrightarrow { a } \). The centre of mass has an acceleration ______________.

(a)

1/2\(\overrightarrow { a } \)

(b)

\(\overrightarrow { a } \)

(c)

2\(\overrightarrow { a } \)

(d)

Zero

Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis xx¹ which is touching to two shells and passing through diameter of third shell. M.I of the system consisting of these three spherial shells about xx¹ axis is ________________.

(a)

3mr²

(b)

4mr²

(c)

16/5mr²

(d)

11/5 mr²

The direction of angular velocity vector is along _______________.

(a)

The tangent to the circular path

(b)

 The outward radius

(c)

The inward radius

(d)

 The axis of rotation

The M.I of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through _____________.

(a)

B

(b)

D

(c)

A

(d)

C

A sphere of radius r is rolling without sliding. What is ratio of rotational K.E and total K.E associated with the sphere?

(a)

2/5

(b)

2/7

(c)

1

(d)

1/2

A sphere rolls down an inclined plane of inclination \(\theta\). What is the acceleration as the sphere reaches bottom?

(a)

5/7 sin\(\theta\)

(b)

3/5 sin \(\theta\)

(c)

2/6 g sin \(\theta\)

(d)

2/5 g sin \(\theta\)

Two rings of radius R & nR made from the same wire have the ratio of moments of intertia about an axis passing through their centre equal to 1 : 8. The value of n is

(a)

2

(b)

2\(\sqrt{2}\)

(c)

4

(d)

1/2

If a solid sphere and solid cylinder of same mass and radius rotate about their own axis the M.I. will be greater for _______________.

(a)

Solid sphere

(b)

Solid cylinder

(c)

Both (a) and (b) 

(d)

Equal both

Analogue of mass in rotational motion is ___________.

(a)

M.l.

(b)

 Angular momentum

(c)

Gyration

(d)

Torque

M.I. of an object does not depend upon ______________.

(a)

Mass of object

(b)

Angular velocity

(c)

Mass distribution  

(d)

Axis of rotation