Question

disc of 얗 radius 25cm & mass 2) A thin un uniform & has a hole of radius 5cm in it. If the centre 19 the circular hole is at a distance of 얼 of 10 om from of the disc, calculate the M.1 of the disc about an axis 1* to its planes & passing through the centre of the hole
​

Answer 1

Answer:

Let mass per unit area of the original disc=σ

Thus mass of original disc=M=σπR2

Radius of smaller disc=R/2.

Thus mass of the smaller disc=σπ(R/2)2=M/4

After the smaller disc has been cut from the original, the remaining portion is considered to be a system of two masses. The two masses are:

M(concentrated at O), and -M(=M/4) concentrated at O'

(The negative sign indicates that this portion has been removed from the original disc.)

Let x be the distance through which the centre of mass of the remaining portion shifts from point O.

The relation between the centres of masses of two masses is given as:

x=(m1r1+m2r2)/(m1+m2)

=(M×0−(M/4)×(R/2))/(M−M/4)=−R/6

(The negative sign indicates that the centre of mass gets shifted toward the left of point O)