The figure shows a man of mass m standing at | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $v_1$ be the velocity of the man with respect to the ground and $v_2$ be the velocity of the trolley with respect to the ground.Since the syst

Vedclass · Accepted Answer

$\frac{m u_{rel}}{m + M}$

Vedclass · Answer

(B) Let $v_1$ be the velocity of the man with respect to the ground and $v_2$ be the velocity of the trolley with respect to the ground.Since the system is on a smooth horizontal surface,there is no external horizontal force acting on the system.Therefore,the momentum of the system is conserved.Initially,the system is at rest,so the initial momentum is $0$.$m v_1 + M v_2 = 0$$v_1 = -\frac{M}{m} v_2$We are given the relative velocity of the man with respect to the trolley as $u_{rel} = v_1 - v_2$.Substituting $v_1$ in the relative velocity equation:$u_{rel} = -\frac{M}{m} v_2 - v_2$$u_{rel} = -v_2 \left( \frac{M}{m} + 1 \right)$$u_{rel} = -v_2 \left( \frac{M + m}{m} \right)$$v_2 = -\frac{m u_{rel}}{M + m}$The magnitude of the velocity of the trolley is $\frac{m u_{rel}}{m + M}$.

Similar Questions

$A$ spacecraft of mass $M$ is moving with a velocity $V$. It suddenly breaks into two parts. One part of mass $m$ comes to rest. What will be the velocity of the other part?

State the law of conservation of momentum.

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

$A$ bomb at rest explodes into three equal fragments. Two of the fragments move at right angles to each other with velocities of $9 \ m s^{-1}$ and $12 \ m s^{-1}$. The magnitude of the velocity of the third fragment is ....... $m s^{-1}$.

Under the influence of mutual internal forces,which of the following is true for a system?

Vedclass Test Series

Exam Paper Generator

Online Exam Module