A couple produces,

(a)

pure rotation

(b)

pure translation

(c)

rotation and translation

(d)

no motion

A system consisting of two masses connected by a massless rod lies along the x axis. If 0.2 kg mass is at a distance x = 0.5m while a 0.3 kg mass is at a distance x = 1m, then the x - co-ordinate of the centre of mass will be at ______________.

(a)

2.5m

(b)

5m

(c)

22.5m

(d)

0.8m

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 rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes,

(a)

L

(b)

L/2

(c)

2L

(d)

L/\(\sqrt{2}\)

A disc of the moment of inertia I_a is rotating in a horizontal plane about its symmetry axis with a constant angular speed \(\omega\). Another disc initially at rest of moment of inertia I_b is dropped coaxially on to the rotating disc. Then, both the discs rotate with the same constant angular speed. The loss of kinetic energy due to friction in this process is,

(a)

\(\frac { 1 }{ 2 } \frac { { I }_{ b }^{ 2 } }{ 2({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(b)

\(\frac { { I }_{ b }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(c)

\(\frac { { ({ I }_{ b }-{ I }_{ a }) }^{ 2 } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

(d)

\(\frac { 1 }{ 2 } \frac { { { I }_{ b }{ I }_{ b } } }{ ({ I }_{ a }+{ I }_{ b }) } { \omega }^{ 2 }\)

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

The speed of the center of a wheel rolling on a horizontal surface is v_o.  A point on the rim in level with the center will be moving at a speed of,

(a)

zero

(b)

v_o

(c)

\(\sqrt{2}\)v_o

(d)

2v_o

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(a)

a line perpendicular to the plane of rotation

(b)

the line making an angle of 45^o to the plane of rotation

(c)

the radius

(d)

tangent to the path

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

The ratio of the radius of gyration of a circular disc to that of circular ring, each of same mass and same radius about their axes is ______________.

(a)

\(\sqrt{3}:\sqrt{2}\)

(b)

\(1:\sqrt{2}\)

(c)

\(\sqrt{2}:1\)

(d)

\(\sqrt{2}:\sqrt{3}\)

A disc is rolling on the inclined plane. What is the ratio of its rotational KE to the total KE?

(a)

1 : 3

(b)

3 : 1

(c)

1 : 2

(d)

2 : 1

Planetary motion in the solar system describes _______________.

(a)

Conservation of energy

(b)

Conservation of linear momentum

(c)

Conservation of angular momentum

(d)

None

M.I. of a ring of mass M and radius R about an axis passing through the centre & perpendicular to the plane is I. What is M.I. about its diameter?

(a)

I

(b)

I/2

(c)

\(I/\sqrt{2}\)

(d)

I + MR²

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

(a)

M.I

(b)

 Angular momentum

(c)

 Angular velocity

(d)

Rotational K.E.

M.I. of a ring of mass M and radius R about an axis passing through the centre & perpendicular to the plane is I. What is M.I. about its diameter?

(a)

I

(b)

I/2

(c)

\(I/\sqrt{2}\)

(d)

I + MR²

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

(a)

M.I

(b)

 Angular momentum

(c)

 Angular velocity

(d)

Rotational K.E.

Centre of mass of the earth and the moon system lies ____________.

(a)

Closer to the earth

(b)

Closer to the moon

(c)

at the mid-point of line joining the earth and the moon

(d)

cannot be predicted

A couple produces ______________.

(a)

linear and rotational motion

(b)

no motion

(c)

purely linear motion

(d)

purely rotational motion

A flywheel is attached to an engine to _____________.

(a)

increase its speed

(b)

decrease its speed

(c)

help in overcoming the dead point

(d)

decrease its energy

Radius of gyration of a body depends upon ______________.

(a)

axis of rotation

(b)

translational motion

(c)

Shape of the body

(d)

area of the body