First slide

Moment of inertia

Question

Three identical rods, each of mass m and length l, form an equilateral triangle. Moment of inertia about one of the sides is

Moderate

A

$\frac{m l^{2}}{4}$
B

$m l^{2}$
C

$\frac{3 m l^{2}}{4}$
D

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

Solution

For first and second rod , take effective length $= l \sin 60^{0}$
$I = I_{1} + I_{2} + I_{3} = \frac{m {(l \sin 60^{0})}^{2}}{3} + \frac{m {(l \sin 60^{0})}^{2}}{3} + 0 = \frac{m l^{2}}{2}$

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