First slide

Moment of intertia

Question

Four spheres each having mass m and radius r are placed with their centres on the four corners of a square of side a. Then the moment of inertia of the system about an axis along one of the sides of the square is

Moderate

A

$\frac{8}{5} {mr}^{2}$
B

$\frac{8}{5} {mr}^{2} + {ma}^{2}$
C

$\frac{8}{5} {mr}^{2} + 2 {ma}^{2}$
D

$\frac{4}{5} {mr}^{2} + 4 {ma}^{2}$

Solution

$I_{AB} = I_{1 AB} + I_{2 AB} + I_{3 AB} + I_{4 AB}$
= $\frac{2}{5} {mr}^{2} + \frac{2}{5} {mr}^{2} (\frac{2}{5} {mr}^{2} + {ma}^{2}) + (\frac{2}{5} {mr}^{2} + {ma}^{2})$
= $\frac{8}{5} {mr}^{2} + 2 {ma}^{2}$

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