Question

Two carts of equal masses were standing still. Each of them had two men of equal masses. From the first cart, a man jumps in north direction with some velocity with respect to the cart and then the second man jumps with the same relative velocity with respect to cart towards the south. The two men on other cart jump simultaneously with the same velocity with respect to cart. The final velocity of both the carts will be same.

- True
- False

Solution

The correct option is **B** False

Let the mass of carts be M and the mass of the men be m. Also the velocities of the men after jumping with respect to cart be u.

In case of the first cart, for the first jump:

(M+2m)×0=m×(u−v)+(M+m)(−v)⇒0=mu−mv−Mv−mv⇒muM+2m=v

For second jump:

(M+m)(−v)=m×(u−v′)−Mv′⇒−(M+m)muM+2m=mu−(m+M)v′⇒v′=mu(2M+3m)(M+2m)(M+m)

In case of second cart, both men will jump simultaneously so the net effect will be zero. Hence, the final velocity of the second cart will be zero.

Thus the above statement is false.

Let the mass of carts be M and the mass of the men be m. Also the velocities of the men after jumping with respect to cart be u.

In case of the first cart, for the first jump:

(M+2m)×0=m×(u−v)+(M+m)(−v)⇒0=mu−mv−Mv−mv⇒muM+2m=v

For second jump:

(M+m)(−v)=m×(u−v′)−Mv′⇒−(M+m)muM+2m=mu−(m+M)v′⇒v′=mu(2M+3m)(M+2m)(M+m)

In case of second cart, both men will jump simultaneously so the net effect will be zero. Hence, the final velocity of the second cart will be zero.

Thus the above statement is false.

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