A circular disc X of radius R is made from an iron plate of thick… - Vidyadip

MCQ

A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t,$ and another plate $y$ of radius $4R$ is made from an iron plate of thickness $\frac {t}{4}$. The ratio of moment of inertia $\frac {I_y}{I_x}$ is

A
$32$
B
$16$
C
$1$
✓
$64$

✓

Answer

Correct option: D.

$64$

d
$\mathrm{I} \propto \mathrm{m} \mathrm{r}^{2} \propto \mathrm \rho\left(\pi \mathrm{r}^{2}\right) \mathrm{tr}^{2}$

$\mathrm{I}=\rho \pi \mathrm{r}^{4} \mathrm{t} \quad$ so $\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{\mathrm{r}_{1}^{4} \mathrm{t}_{1}}{\mathrm{r}_{2}^{4} \mathrm{t}_{2}}$

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