First slide

Moment of inertia

Question

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is:

Easy

A

2/3
B

1/2
C

1/4
D

1/8

Solution

$\begin{array}{l} M O I t h r o u g h O = I_{0} = \frac{1}{12} m (a^{2} + b^{2}) \\ M O I t h r o u g h O' = I_{0}^{'} = \frac{1}{3} m (a^{2} + b^{2}) \\ ∴ \frac{I_{0}}{I_{0}^{'}} = \frac{\frac{1}{12}}{\frac{1}{3}} = \frac{1}{4} \end{array}$

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