Question

A metallic circular plate is rotating about its axis without friction. If the radius of plate expands by $0.1\%$, then the $\%$ change in its moment of inertia is :

• A. increases by $0.1\%$
• B. decreases by $0.1\%$
• C. increases by $0.2\%$
• D. decreases by $0.2\%$

Answer 1

The correct option is C increases by $0.2\%$

We know $I=\frac{M{R}^2}{2}$

Now $dI=MRdR$ (on differentiating both the sides)

$dR=0.001R$ (given)

So $dI=0.001M{R}^2=0.1\times 2I$

So $\frac{dI}{I}=0.002or0.2$%