First slide

Moment of intertia

Question

ABC is an equilateral triangular sheet of mass m and side length $l$ . Find its moment of inertia about an axis passing through the centre of mass of the sheet and parallel to the side BC.

Difficult

A

$\frac{m l^{2}}{24}$
B

$\frac{m l^{2}}{12}$
C

$\frac{m l^{2}}{8}$
D

$\frac{m l^{2}}{48}$

Solution

Altitude of the triangle
$h = l s i n 60^{o} = \frac{\sqrt{3} l}{2}$
$∴ O M = \frac{h}{3} = \frac{l}{2 \sqrt{3}}$
Now, $I_{PQ} = I_{BC} - m x {(OM)}^{2}$
$= \frac{1}{6} m {(\frac{\sqrt{3} l}{2})}^{2} - m {(\frac{l}{2 \sqrt{3}})}^{2} = \frac{1}{24} m l^{2}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App