First slide

Moment of intertia

Question

A rhombus ABCD is made of four identical thin wires each of mass m and length l. as shown in figure. Then moment of inertia of the rhombus about side AB is

Difficult

A

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

$\frac{5}{4} m l^{2}$
C

$\frac{1}{4} m l^{2}$
D

$\frac{1}{3} m l^{2}$

Solution

$I = I_{A B} + I_{B C} = I_{C D} + I_{A D}$
$= O + \frac{1}{3} m l^{2} \sin^{2} 60^{o} + m {(l \sin 60^{o})}^{2} + \frac{1}{3} m l^{2} \sin^{2} 60^{o}$
$= \frac{1}{2} m l^{2} + \frac{3}{4} m l^{2} = \frac{5}{4} m l^{2}$

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