First slide

Location of centre on mass for multiple point masses

Question

The centre of mass of a system of two particles of masses $m_{1} and m_{2}$ is at a distance $d_{1}$ from $m_{1}$ and at a distance $d_{2}$ from mass $m_{2}$ such that

Moderate

A

$\frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1}}$
B

$\frac{d_{1}}{d_{2}} = \frac{m_{1}}{m_{2}}$
C

$\frac{d_{1}}{d_{2}} = \frac{m_{1}}{m_{1} + m_{2}}$
D

$\frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1} + m_{2}}$

Solution

Refer figure,
The distances of centre of mass CM from masses $m_{1} and m_{2}$ are
$d_{1} = \frac{m^{2} d}{m_{1} + m_{2}} and d_{2} = \frac{m_{1} d}{m_{1} + m_{2}} ∴ \frac{d_{1}}{d_{2}} = \frac{m_{2}}{m_{1}}$

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