First slide

Motion of centre of mass

Question

Two bodies of masses 5kg and 3kg are moving towards each other with 2ms^–1 and 4ms^–1 respectively. Then velocity of centre of mass is

Easy

A

0.25ms^-1 towards 3kg
B

0.5ms^-1 towards 5kg
C

0.25ms^-1 towards 5kg
D

0.5ms^-1 towards 3kg

Solution

m₁ = 5kg, m₂ = 3kg, v₁ = 2m/s, v₂ = –4m/s
$\large {v_{cm}} = \frac{{{m_1}{v_1} + {m_2}{v_2}}}{{{m_1} + {m_2}}} = \frac{{5\left( 2 \right) + 3\left( { - 4} \right)}}{8} = - \frac{2}{8}$
= -0.25m/s = 0.25m/s toward 5kg
$\large {v_c} = \frac{{{m_1}{v_1} + {m_2}{v_2}}}{{{m_1} + {m_2}}}$

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