First slide

Moment of intertia

Question

A light rod of length l has two masses $m_{1} and m_{2}$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

Moderate

A

$(m_{1} + m_{2}) l^{2}$
B

$\sqrt{m_{1} m_{2}} l^{2}$
C

$\frac{m_{1} m_{2}}{m_{1} + m_{2}} l^{2}$
D

$\frac{m_{1} + m_{2}}{m_{1} m_{2}} l^{2}$

Solution

$r_{1} = \frac{m_{2} l}{m_{1} + m_{2}}, r_{2} = \frac{m_{1} l}{m_{1} + m_{2}}$
$I_{cm} = m_{1} {r^{2}}_{1} + m_{2} {r^{2}}_{2} = \frac{m_{1} m_{2}}{m_{1} + m_{2}} l^{2}$

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