Question

A girl of mass 50 kg standing on a rail road car of mass 75 kg moving with velocity 20 m/s. Now, the girl begins to run with velocity of 10 m/s with respect to the car in the same direction. as that of the car. Velocity of the car at this instant will be

• A. 20 m/s
• B. 24 m/s
• C. 16 m/s
• D. 18 m/s

Answer 1

The correct option is C 16 m/s

By the law of conservation of momentum, under the action of no external forces, the momentum of a system is constant.

Consider the system of the girl and the car. Net external force acting on the system is zero.

Hence, the momentum of the system is conserved i.e., $P_{g,i}+P_{c,i}=P_{g,f}+P_{c,f}$

Consider an observer on the ground.

Initial velocity of the car is $v_{c,i}=20\text{m/s}$

Initial velocity of the girl is $v_{g,i}=20\text{m/s}$

Thus, Initial momentum is $P_i=m_g{v}_{g,i}+m_c{v}_{c,i}=50\times 20+75\times 20=2500\text{kg m/s}$

Let the final velocity of the car be $v_{c,f}=v$

Given that final velocity of the girl wrt car is $10\text{m/s}$ in the same direction.

Hence the final velocity of the girl as seen by the observer is $v_{g,f}=v+10$

Thus, the final momentum of the system is $P_f=m_g{v}_{g,f}+m_c{v}_{c,f}=50\times (v+10)+75\times v=125v+500$

But, as $P_i=P_f\Rightarrow 125v+500=2500$

$\Rightarrow v=16\text{m/s}$