Question

1
27. Moment of inertia of a body is a measure of its rotational inertia.
(a) What are the factors on which moment of inertia of a rigid body depends ?
(b) State the theorem that helps to find the moment of inertia of a disc about any
diameter.
(c) A disc and a ring of same outer radii have the same mass. Which will have the
larger moment of inertia about an axis passing through the centre and
perpendicular to the planes ?
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Answer 1

Answer:

Moment of inertia. Moment of inertia, in physics, quantitative measure of the rotational inertia of a body—i.e., the opposition that the body exhibits to having its speed of rotation about an axis altered by the application of a torque (turning force).

Answer 2

The answers regarding the moment of inertia are :

(a) The factors on which the moment of inertia of a rigid body depends are:

1. Mass of the object (m)
2. Distance of the centre of mass from the axis (r)

Moment of inertia, I = m×r²

(b) The theorems that help to find the moment of inertia of a disc about any diameter are Perpendicular axis theorem and Parallel axis theorem.

(c) The ring will have a larger moment of inertia about an axis passing through the centre and perpendicular to the planes.

The disc and the ring have same mass = m

The outer radius of these two is also same = r

For the disc,

Moment of inertia about an axis passing through the centre and perpendicular to the planes = m×r²

For the ring,

Moment of inertia about an axis passing through the centre and perpendicular to the planes = $\frac{1}{2}$×m×r²

So, The ring will have a larger moment of inertia about an axis passing through the centre and perpendicular to the planes.