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

Answer

B

Explanation

When ring is at maximum height, the wedge and ring have same `x` component of velocity. In the absence of friction between ring and wedge surface, angular velocity of ring remains constant. From conservation of energy, we get `1/2m upsilon^(2)+1/2I'omega^(2)=1/2 m upsilon'^(2)+1/2 I omega^(2)+1/2m upsilon'^(2)+mgh`
Where `upsilon` is final common velocity,
`upsilon'=(upsilon)/2, h=(upsilon^(2))/(4g)`