A strange cat with a mass `m_(c )` is sitting at rest on the left sled of a pair of identical sleds. The sleds hace mass `m_(s)` and sit on frictionless ice. Suddenly, the cat leaps to the right sled, traveling with a horizontal speed `v_(cg)` measured with respect ot the groun. The instant the cat reaches the right sled, it turns around and leaps back to the left sled. The horizontal component of the cat's speed is again `v_(cg)` measured with respect to the ground. The final speed of right sled in terms of the masses of the cat and sleds and the cat's leaping speed is (The cat remains on the left sled after its return) :-

Options

A. `(2m_(c )v_(cg))/(m_(s) + m_(c ))`
B. `(2m_(c )v_(cg))/(m_(s))`
C. `(m_(c )v_(cg))/(m_(s) + m_(c ))`
D. `(m_(c )v_(cg))/(m_(s))`

Answer

B

Explanation

For system (cat `+` right sled )
`F_(ex) = 0`
Let `v_(R )` be velocity (final) after cat jump off right shed.
`P_(1) = P_(f)`
`m_(c ) v_(eg) - m_(5) v_(R ) - m_(c ) v_(eg)`
`v_(R ) = (2m_(c ) v_(eg))/(m_(s))`