Question

$I$ is moment of inertia of a uniform circular plate of radius $R$ about its natural axis. If a circular hole of diameter $R$ is made in that plate such that the centre of hole coincides with centre of plate then the moment of inertia of remainder plate about same axis is:

• A. $\frac{I}{16}$
• B. $\frac{15I}{16}$
• C. $\frac{I}{8}$
• D. $\frac{7I}{8}$

Answer 1

The correct option is B $\frac{15I}{16}$

Radius of the hole = R/2

Mass corresponding to radius $\Rightarrow$ M $\propto$ $R^2$

So, mass corresponding to radius = R/2 $\Rightarrow$ M/4

M.I. of remainder of the plate + MI of the hole = MI of the plate

$I_R+I_H=I$

$\Rightarrow I_R+\frac{M}{4}{\left(\frac{R}{2}\right)}^2=M{R}^2$

$\Rightarrow I_R=\frac{15}{16}M{R}^2$