Question

A wagon weighing $1000kg$ is moving with a velocity $50km/h$ on smooth horizontal rails. A mass of $250kg$ is dropped into it. The velocity with which it moves now is (in km/h)

• A. $40$
  
• B. $50$
  
• C. $60$
  
• D. $20$
  

Answer 1

Answer: (A)

$40$

Mass of wagon $m=1000kg$

Initial velocity of wagon $v=50km/h$

Initial linear momentum of the system $P_i=mv=1000\times 50=5\times {10}^{4}kgkm/h$

Let the final velocity (wagon+ mass dropped) system be $V$.

Final linear momentum of the system $P_f=(m+M)V=(1000+250)V=1250V$

Using conservation of linear momentum, $P_f=P_i$

$\therefore$ $1250V=5\times {10}^4$

$⟹$ $V=\frac{5\times {10}^4}{1250}=40km/h$