First slide

Motion of centre of mass

Question

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

Moderate

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

$\large ({m_1} + {m_2}){x_c} = {m_1}{x_1} + {m_2}{x_2}$
$\large \Delta {X_{CM}} = 0 \Rightarrow {m_1}\Delta {X_1} + {m_2}\Delta {X_2} = 0$
$\large {m_1}\Delta {X_1} = - {m_2}\Delta {X_2}$
$\large \Delta {X_2} = \frac{{ - {m_1}\Delta {X_2}}}{{{m_2}}} = \frac{{ - 2}}{3}cm$
2/3 cm towards 10kg

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