First slide

Motion of centre of mass

Question

A shell in flight explodes into n equal fragments, k of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

Moderate

A

g
B

(n-k)g
C

$\large \frac {(n-k)g}{k}$
D

$\large \frac {(n-k)g}{n}$

Solution

If 'k' fragments reaches ground So, their acceleration =0
$\large {a_{CM}} = \frac{{{m_1}{a_1} + ...... + {m_2}{a_2}}}{{{m_1} + ...... + mn}}$
$\large = \frac{{\left[ {mg + ....... + \left( {n - k} \right)terms} \right] + \left[ {m\left( 0 \right) + ...... + kterms} \right]}}{{nm}}$
$\large = \frac{{\left( {n - k} \right)mg}}{{nm}} = \frac{{\left( {n - k} \right)g}}{n}$

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