A metallic solid sphere is rotating about its diameter as axis of… - Vidyadip

MCQ

A metallic solid sphere is rotating about its diameter as axis of rotation. If the temperature is increased by 200°C, the percentage increase in its moment of inertia is : (coefficient of linear expansion of the metal = 10-5/°C)

A
$0.1$
B
$0.2$
C
$0.3$
✓
$0.4$

✓

Answer

Correct option: D.

$0.4$

$ 0.4$
Solution :
$I =\frac{2}{5} MR ^2$
$\frac{\Delta I }{ I } =2 \frac{\Delta R }{ R }=\frac{2 R \alpha \Delta t}{ R }=2 \alpha \Delta t $
$\frac{\Delta I }{ I } =2 \times 10^{-5} \times 200=4 \times 10^{-3}$
{ Percentage increase }$=4 \times 10^{-3} \times 100=0.4$

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