Consider two skaters `A` and `B` initially at rest on ice -(friction is negligible) with `A` holding a ball. A has greater mass than `B` and the ball has some significant mass. A throws the ball to `B`. `B` catches it and throws it back to `A` who catches it again. The magnitudes of the skater's (excluding ball) final velocities, A momentum and kinetic energies (denoted below as `v, p` and `K` respectively) are related as

Options

A. `v_(A)=v_(0)`
B. `v_(A)ltv_(B),p_(A)ltp_(B)`
C. `p_(A)=p_(B),K_(A)ltK_(B)`
D. `p_(A)ltp_(B),K_(A)ltK_(B)`

Answer

B, D

Explanation

Let after the process of catching is over, final velocites are as shown.
`mrarr` mass of ball
`m_(1)rarr` mass of `B`
`m_(2)rarr` mass of `B`

Apply conservation of momentum for entire system.
`0=-(m_(1)+m)v_(A)+m_(2)v_(B)`
`implies (m_(1)+m)v_(A)=m_(2)v_(B)`.........i
Hence `m_(1)gtm_(2)`
`impliesv_(B)/v_(A)=(m_(1)+m)/m_(1)gt1impliesv_(B)gtv_(A)`
`p_(A)=m_(1)v_(A), p_(B)=m_(2)v_(B)`
clearly from and ii `p_(B)gtp_(A)`
`K_(A)=1/2m_(1)v_(A)^(2)=1/2p_(A)v_(A)`
`K_(B)=1/2m_(2)v_(B)^(2)=1/2p_(B)v_(B)`
clearly `K_(B)gtK_(A)`