Question

A shell of mass $m$ moving with velocity $V$ suddenly breaks into $2$ pieces. The part having mass $m/4$ remains stationary. The velocity of the other shell will be:

• A. $V$
• B. $2V$
• C. $3/4V$
• D. $4/3V$

Answer 1

The correct option is D $4/3V$

Mass of the one part which remains at rest is $\frac{m}{4}$.

Thus mass of other shell is $\frac{3m}{4}$.

Using conservation of linear momentum : $P_{initial}=P_{final}$

$mV=\frac{m}{4}\times 0+\frac{3m}{4}{V}_2$

Or $mV=\frac{3m}{4}{V}_2$

$⟹$ $V_2=\frac{4V}{3}$