Question

The moment of inertia of a uniform circular disc is minimum about an axis perpendicular to the disc and passing through the point
$
  (1)\;\,{\text{A}} \\
  {\text{(2) C}} \\
  {\text{(3) D}} \\
  {\text{(4) B}} \\
 $

Answer 1

Hint: The moment of inertia of a uniform circular disc about an axis passing through its centre and perpendicular to it can be given by - $I = M{R^2}$ where “I” is the moment of inertia, M is the mass and R is the distance from the axis of the motion.

Complete step by step answer:
The moment of inertia of the uniform circular disc can be given by –
$I = M{R^2}$
By using the theorem of parallel axis which states that the moment of inertia (I) of the body about an axis is parallel to the body passing through its centre is always equal to the sum of the moment of inertia of the body about the axis passing through the centre and is the product of mass (M) and the square of the distance (d) between the two axes.
$I = M{R^2} + M{d^2}$
From the above equation as the distance of the point from the centre increases there will be an increase in its moment of inertia.
The point more close to the centre of the disc decreases the moment of inertia.
From the given diagram, the minimum moment of inertia is at point B.

So, the correct answer is “Option 4”.

Note:
The moment of inertia is the property of the body by its desirable quality of its mass and state of motion whether it is at rest or in motion. We experience the property of inertia almost every day. For example- The rolling ball comes to halt or is stopped by an external force.