First slide

Moment of inertia

Question

An arrangement of rods each of mass m and length l are welded (where ever required) to form a shape as shown. The moment of inertia about an axis passing through point C and perpendicular to the plane of figure is:

Moderate

A

$m l^{2}$
B

$\frac{3}{2} m l^{2}$
C

$\frac{9}{2} m l^{2}$
D

$3 m l^{2}$

Solution

$I = 4 (\frac{m l^{2}}{3}) + 2 [\frac{m l^{2}}{12} + m {(\frac{\sqrt{3} l}{2})}^{2}] = 3 m l^{2}$
$∵$ Moment of inertia of the rod about its end = $\frac{m l^{2}}{3}$
Moment of inertia of a thin rod about its centre and perpendicular to its length= $\frac{m l^{2}}{12}$
Moment of inertia of rods placed horizontally is given by = $\frac{m l^{2}}{12} + m x^{2}$ where x= $\frac{l \sqrt{3}}{2}$

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