Question

Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track (figure). The person on left jumps to the left with a horizontal speed u with respect to the state of the car before the jump. Therefore, the other person jumps to the right, again with the same horizontal speed u with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off.

• A. towards left
• B. towards left
• C. towards right
• D. towards right

Answer 1

The correct option is A

towards left

Two persons each of mass m are standing at the two extremes of a railroad car of mass m resting on a smooth track.

Case - I

Let the velocity of the railroad car with respect to the earth is V after the jump of the left man.

0 = - mu + (M + m) V

$\Rightarrow V=\frac{mu}{M+m}$ Towards right

Case - II

When the man on the right jumps , the velocity of it with respect to the car is u.

$\therefore 0=mu-Mv\prime$

$\Rightarrow v\prime =\frac{mu}{M}$

(V' is the change is velocity of the platform when platform itself is taken as reference assuming the car

to be at rest )

$\therefore$ So , net velocity towards left ( i.e. the velocity of the car with respect to the earth )

$=\frac{mu}{M}-\frac{mu}{M+m}=\frac{mMu+m^{2}u-Mmu}{M(M+m)}=\frac{m^{2}u}{M(M+m)}$