Q. 16

# The surface density (mass/area) of a circular disc of radius α depends on the distance from the centre as p(r) =A +Br. Find its moment of inertia about the line perpendicular to the plane of the disc through its centre.

Answer :

The moment of inertia =

Given

The radius of the circular disc is “a”, and the distance from the center to the edge of the disc is given as. Hence to find moment of inertia we find the relationship mass and moment of inertia in terms of area.

Formula Used

The inertia of the body for a point of mass is the product of the square of the radius with the mass of the body. The formula is

where

I is the moment of Inertia, A is the area of the object and r is the radius of the object.

Explanation

The moment of inertia of a disc is

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The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?

Physics - ExemplarThe surface density (mass/area) of a circular disc of radius α depends on the distance from the centre as p(r) =A +Br. Find its moment of inertia about the line perpendicular to the plane of the disc through its centre.

HC Verma - Concepts of Physics Part 1