A small object of uniform density rolls up a curved surface with an initial velocity 'w'. It reaches up to a maximum height of `(3u^(2))/(4g)` with respect to initial position. The object is:

Options

A. ring
B. solid sphere
C. hallow sphere
D. disc.

Answer

D

Explanation

We can apply conservation of mechanical energy as follows:
Loss in K.E. = Gain in gravitational potential energy
`(1)/(2)m""u^(2)+(1)/(2)I((u)/(r))^(2)=mg((3u^(2))/(4g))`
`implies(1)/(2)I((u)/(r))^(2)=(3)/(4)m""u^(2)-(1)/(2)m""u^(2)=(1)/(4)m""u^(2)`
`impliesI=(1)/(2)mr^(2)`
We have got moment of inertia of disc hence given object must be disc. Option (d) is correct.