Question

A man weighing $80kg$ is standing on a trolley weighing $320kg$. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley along the rails at speed $1m/s^{-1}$, then after $4s$ his displacement relative to the ground will be:

• A. $5m$
• B. $4.8m$
• C. $3.2m$
• D. $3.0m$

Answer 1

The correct option is C $3.2m$

To conserve the momentum, trolly will move in the direction opposite to man's movement. let trollys velocity is v and its mass is m. Let man's velocity is V and his mass is M, then we have $m\times v=-(M+m)\times V$..................(1)

we have $m=320kg$, $M=80kg$, $V=1m/s$ by substituting this value sin (1),

we get $v=-0.2m/s$.

Since man has moved for $4s$, distance moved by truly $-0.2times4=-0.8m$man has moved 4m but trolly has moved 1 min opposite direction. hence displacement of a man with respect to ground is$4-0.8=3.2m$

Hence, Option $C$ is correct.