Question

A disc is rotating about its own axis with angular frequency $100rpm$. When a mass of $100g$ is placed at $10cm$ from its centre then its angular frequency becomes $50rpm$. The moment of inertia of the disc is:

• A. $5\times {10}^{4}gc{m}^2$
• B. ${10}^{4}gc{m}^2$
• C. ${10}^{3}gc{m}^2$
• D. ${10}^{5}gs{m}^2$

Answer 1

The correct option is B ${10}^{4}gc{m}^2$

$w_1$ = $100rpm$

$w_2$ = $50rpm$

When a mass of 100 g is paced at 10 cm from its centre of disc, then moment of inertia

$I_2$ = $I_1$ + $m{r}^2$

$I_2$ = $I_1$ + $100\times \left({10}^2\right)$

$I_2$ = ($I_1$ + ${10}^4$) $gc{m}^2$

By using law of conservation of angular momentum,

$I_1{w}_2$ = $I_2{w}_2$

$I_1\times 100$ = $(I_1+{10}^4)\times 50$

$I_1\times 100$ = $(50I_1+5\times {10}^5$

$100I_1-50I_2=5\times {10}^5$

$I_1={10}^{4}gc{m}^2$