Question

Consider the following two statements A and B and identify the correct choice.
A) The moment of inertia of a rigid body is independent of its angular velocity.
B) The radius of gyration of a rotating metallic disc is dependent on its temperature.

• A. A is true but B is false
• B. A is false but B is true
• C. Both A and B are true
• D. Both A and B are false

Answer 1

The correct option is C Both A and B are true

(A) Moment of inertia of the rigid body only dependent on the mass of the body and position of the axis of rotation. It is independent of the angular velocity.
(B) $I=m{k}^2$

$k=\sqrt{\frac{T}{m}}(k=$radius of gyration)

$I_{dist}=\frac{m{R}^2}{2}$

$k=\frac{R}{\sqrt{2}}$

and Radius of the metallic disc is dependent on the temperature, because

$A=A_0(1+B\Delta T)$ (Equation of thermal expansion)

$\pi r^2=\pi R_0^2(1+B\Delta T)$

$r=R_0\sqrt{1+B\Delta T}$