Question

A solid cylinder is rotating about its natural axis. Due to decrease in atmospheric temperature if length and radius of cylinder both contract by $0.2\%$ each, then the $\%$ decrease in its moment of inertia is :

• A. $0.2\%$
• B. $0.4\%$
• C. $0.6\%$
• D. $0.8\%$

Answer 1

Answer: (B)

$0.4\%$

So we can see
$I_z\propto r^2$
So change in height will not affect the moment of inertia of the cylinder
new $R=$$R(1-\left(\frac{0.02}{10}\right))=\left(0.98\right)R$
Mass is still the same
$MOI=\frac{M{R}^2}{2}(1-\frac{0.02}{10})$
$\frac{M{R}^2}{2}(1-2\times \frac{02}{10}+(.02{)}^2)$
$\frac{M{R}^2}{2}(1-\frac{0.04}{10})$
$\left(△MOI\right)$$\%=\frac{0.04}{10}\times 100$
$=0.4$