Question

A shell of mass is moving with velocity $v$ suddenly breaks into two pieces; the part having mass $\frac{m}{3}$ remains stationary. The velocity of another part will be:

• A. $\frac{2v}{3}$
• B. $\frac{3v}{2}$
• C. $\frac{8v}{19}$
• D. none of these

Answer 1

Answer: (B)

$\frac{3v}{2}$

Momentum of the system initially $P_i=mv$

Mass of the first part is $\frac{m}{3}$

Mass of other part $=m-\frac{m}{3}=\frac{2m}{3}$

Momentum of the system finally $P_f=\frac{m}{3}\left(0\right)+\frac{2m}{3}V=\frac{2m}{3}V$

Using conservation of linear momentum : $P_i=P_f$

$\therefore$ $mv=\frac{2m}{3}V$

$⟹V=\frac{3}{2}v$