First slide

Moment of intertia

Question

Fig. shows a uniform solid block of mass M and
edge length a, b and c. The moment of inertia of the block about an axis through one edge and perpendicular (as shown) to the large face is

Moderate

A

$\frac{M}{3} (a^{2} + b^{2})$
B

$\frac{M}{4} (a^{2} + b^{2})$
C

$\frac{7 M}{12} (a^{2} + b^{2})$
D

$\frac{M}{12} (a^{2} + b^{2})$

Solution

The moment of inertia about centre of gravity is given by
$I_{C . G .} = M [\frac{a^{2} + b^{2}}{12}]$
To obtain the moment of inertia about the required axis, we apply the theorem of parallel axes, hence
$\begin{array}{l} I_{required axis} = I_{C . G .} + M (OA)^{2} \\ = M (\frac{a^{2} + b^{2}}{12}) + M (\frac{a^{2} + b^{2}}{4}) \\ = M (\frac{a^{2} + b^{2}}{3}) \end{array}$

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