Moment Of Inertia

The moment of inertia of a uniform circular disc of radius and mass about an axis touching the disc at its diameter and normal to the disc is:
1. $M{R}^2$

2. $\frac{2}{5}M{R}^2$

3. $\frac{3}{2}M{R}^2$

4. $\frac{1}{2}M{R}^2$

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

1.		2.
3.		4.

A thin rod of length and mass is bent at its midpoint into two halves so that the angle between them is . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:
1.
2.
3.
4.

The moment of inertia of a thin uniform rod of mass and length about an axis passing through its mid-point and perpendicular to its length is . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:
1.
2.
3.
4.

Point masses and are placed at the opposite ends of a rigid rod of length and negligible mass. The rod is set into rotation about an axis perpendicular to it. The position of a point on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity  is minimum is given by:

1.		2.
3.		4.

A light rod of length has two masses, and attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is:

1.		2.
3.		4.

A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy (K_t) as well as rotational kinetic energy (K_r) simultaneously. The ratio K_t : (K_t + K_r) for the sphere will be:

1. 7:10

2. 5:7

3. 10:7

4. 2:5

From a circular ring of mass and radius an arc corresponding to a sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is times The value of will be:

1.		2.
3.		4.

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is:

1.		2.
3.		4.

The ratio of the radius of gyration of a solid sphere of mass and radius about its own axis to the radius of gyration of the thin hollow sphere of the same mass and radius about its axis is:
1.
2.
3.
4.

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is in the direction shown, which one of the following options is correct ( and are any highest and lowest points on the wheel, respectively)?

1.	Point moves faster than point .
2.	Both the points and move with equal speed.
3.	Point has zero speed.
4.	Point moves slower than point .

The moment of inertia of a thin rod about an axis passing through its mid-point and perpendicular to the rod is The length of the rod is nearly:
1.
2.
3.
4.

A sphere of radius is cut from a larger solid sphere of radius as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the -axis is:

1.		2.
3.		4.