First slide

Location of centre on mass for multiple point masses

Question

Masses of 2 kg each are placed at the corners B and A of a rectangular plate ABCD as shown in the figure. A mass of 8 kg has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at:

Moderate

A

1 m from O on OE
B

2 m from O on OF
C

2 m from O on OG
D

2 m from O on OH

Solution

$x_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
$\Rightarrow 0 = \frac{2 (- 2) + 2 (- 2) + 8 x_{2}}{2 + 2 + 8}$
$\Rightarrow x_{3} = 1 m$

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