A trolley was moving horizontally on a smooth ground with velocity `v` with respect to the earth. Suddenly a man starts running from rear end of the trolley with a velocity `(3//2)v` with respect to the trolley. After reaching the other end, the man turns back and continues running with a velocity `(3//2)v` with respect to trolley in opposite direction. If the length of the trolley is L, find the displacement of the man with respect to earth when he reaches the starting point on the trolley. Mass of the trolley is equal to the mass of the man.

Options

A. `4/3L`
B. `2/3L`
C. `(5L)/3`
D. `1.5L`

Answer

C

Explanation

Since velocity of man w.r.t. trolly is greater than velolcity of trolly w.r.t earth, after the man turns back displacement of the man will decrease, so maximum displacement will be at the moment when man turns back.
`:. t=L/(1.5V)`
displacement `=(v+1.5v)t`
`=2.5vL/(1.5v)=5/3L`