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

(A) Let $v_1$ be the velocity of the man and $v_2$ be the velocity of the trolley with respect to the ground.Since the system is on a smooth horizonta

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let $v_1$ be the velocity of the man 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 $0$.$m v_1 + M v_2 = 0 \implies v_2 = -\frac{m}{M} v_1$.The relative velocity of the man with respect to the trolley is given by $u_{rel} = v_1 - v_2$.Substituting $v_2$ in the equation: $u_{rel} = v_1 - (-\frac{m}{M} v_1) = v_1 (1 + \frac{m}{M}) = v_1 (\frac{M + m}{M})$.Solving for $v_1$,we get $v_1 = \frac{M u_{rel}}{M + m}$.

Similar Questions

$A$ bullet of mass $m$ moving with velocity $v$ is fired into a wooden block of mass $M$. If the bullet remains embedded in the block,the final velocity of the system is:

Three masses $m$,$2m$,and $3m$ are moving in the $x-y$ plane with speeds $3u$,$2u$,and $u$ respectively,as shown in the figure. The three masses collide at the same point $P$ and stick together. The velocity of the resulting mass will be

$A$ shell of mass $0.020 \; kg$ is fired by a gun of mass $100 \; kg$. If the muzzle speed of the shell is $80 \; m s^{-1}$,what is the recoil speed in $m/s$ of the gun?

$A$ body of mass $M$ moving with velocity $V$ explodes into two equal parts. If one part comes to rest and the other part moves with velocity $v_{0}$,what would be the value of $v_{0}$?

$A$ person of mass $80 \ kg$ is standing on a trolley of mass $320 \ kg$. The trolley is at rest on a frictionless horizontal rail. If the person walks on the trolley at a speed of $1 \ m/s$,what will be their displacement relative to the ground after $4 \ s$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module