Question

Ratio of moment of inertia, $I_1:I_2$ of a uniform square plate about shown axes is

• A. $7:1$
• B. $1:3$
• C. $3:1$
• D. $1:7$

Answer 1

The correct option is D $1:7$

For uniform square plate,
$I_1=\frac{m{a}^2}{12}$ ... (1)

$I_2=\frac{m{a}^2}{12}+m{d}^2$
[Parallel axis theorem]
$=\frac{m{a}^2}{12}+m\times \frac{a^2}{2}$
$=\frac{7m{a}^2}{12}$... (2)
From (1) and (2)
$I_1:I_2=\frac{I_1}{I_2}=\frac{\frac{m{a}^2}{12}}{\frac{7m{a}^2}{12}}$
$I_1:I_2=1:7$
$\therefore$ Ratio of moment of inertia, $I_1:I_2$ is $1:7$