First slide

Location of centre on mass for multiple point masses

Question

Three masses are placed on the x-axis: 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is

Easy

A

40 cm
B

45 cm
C

50 cm
D

30 cm

Solution

$x_{CM} = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
= $\frac{300 (0) + 500 (40) + 400 (70)}{300 + 500 + 400}$
= $\frac{20000 + 28000}{1200} = \frac{48000}{1200} = 40 cm$

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