In the figure shown, a ring `A` is initially rolling without sliding with a velocity `1`, on the horizontal surface of the body `B` (of same mass as `A`). All surfaces arc smooth. `B` has no initial velocity. What will be the maximum height reached by `A` on `B`?

Options

A. `(3v^(2))/(4g)`
B. `(v^(2))/(4g)`
C. `(v^(2))/(2g)`
D. `(v^(2))/(3g)`

Answer

B

Explanation

When the ring is at the maximum height, the wedge and the ring have the same horizontal component of velocity. As all the surface are smooth, in the absence of friction between the ring and wedge and surface angular velocity of the ring raemains constant.From conservation of mechanical energy
`1/2Mv^(2)+1/2Iomega^(2)=1/2Mv_(1)^(2)+1/2Iomega^(2)+1/2Mv_(1)^(2)+mgh`
where `v_(1)`=final common velocity `=v/2` `h=(v^(2))/(4g)`