First slide

Moment of intertia

Question

Three identical thin rods, each of mass m and length l, are joined to form an equilateral triangular frame. The moment of inertia of the frame about an axis parallel to its one side and passing through the opposite vertex is

Moderate

A

$\frac{5 {ml}^{2}}{2}$
B

$\frac{5 {ml}^{2}}{4}$
C

$\frac{3 {ml}^{2}}{2}$
D

$\frac{5 {ml}^{2}}{3}$

Solution

About OO’
$I_{AC} = I_{BC} = \frac{{ml}^{2}}{3} \sin^{2} 60^{0} = \frac{{ml}^{2}}{4}$
MI of the rod AB about OO’
$I_{AB} = m {(\frac{l \sqrt{3}}{2})}^{2} = \frac{3 {ml}^{2}}{4}$
$I = I_{AC} + I_{BC} + I_{AB} = \frac{5 {ml}^{2}}{4}$

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