PhysicsTwo particles of masses 10kg and 30kg are lying on a straight line. The 10kg mass is shifted towards the 30kg mass by a distance of 2cm. By what distance should the 30kg mass be shifted so that the position of their centre of mass does not change

Two particles of masses 10kg and 30kg are lying on a straight line. The 10kg mass is shifted towards the 30kg mass by a distance of 2cm. By what distance should the 30kg mass be shifted so that the position of their centre of mass does not change

A
2/3 cm towards 10kg
B
2/3 cm away from 10 kg
C
3/2 cm towards 10 kg
D
3/2 cm away from 10 kg

Solution:

$∆ X_{CM} = 0 \Rightarrow \frac{m_{1} ∆ X_{1} + m_{2} ∆ X_{2}}{m_{1} + m_{2}} = 0$

$m_{1} ∆ X_{1} + m_{2} ∆ X_{2} = 0$

$∆ X_{2} = \frac{- m ∆ X_{2}}{m_{2}} = \frac{- 2}{3} cm$
2/3cm towards 10 kg

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