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Displacement of COM:Application

A body fallin...

Question

A body falling vertically downwards under gravity breaks in two parts of unequal masses. The centre of mass of the two parts taken together:-

A

Shifts horizontally towards heavier piece

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B

Shifts horizontally towards lighter piece

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C

Doesn't shift horizontally

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D

Shift horizontally if initial speed is zero

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Solution

The correct option is C Shifts horizontally towards heavier piece
Body is falling vertically downwards as there is no horizontal force in x-direction. So x cordinate of $X_{c m}$ not change
$\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}} = X_{c m}$
$X_{c m} = 0$
then,
$m_{1} x_{1} = - m_{2} x_{2}$
let, $m_{1} < m_{2}$
So, $x_{1} > x_{2}$

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