First slide

Moment of intertia

Question

Two spheres each of mass M and radius $\frac{R}{2}$ are connected at their centres with a mass less rod of length 2R. What will be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod?

Moderate

A

$\frac{21 {MR}^{2}}{5}$
B

$\frac{2 {MR}^{2}}{5}$
C

$\frac{5 {MR}^{2}}{2}$
D

$\frac{5 {MR}^{2}}{21}$

Solution

$I_{AB} = I_{1 AB} + I_{2 AB}$
= $\frac{2}{5} M {(\frac{R}{2})}^{2} + \frac{2}{5} M {(\frac{R}{2})}^{2} + M {(2 R)}^{2}$
= $\frac{21}{5} {MR}^{2}$

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