A small object of uniform density rolls up a curved surface with an initial velocity v. it reaches up to a maximum height of `(3v^2)/(4g)

with respect to the initial position. The object is

Options

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

Answer

C

Explanation

By the law of conservation,
`PE = KE_("rolling")`
`mgh = (1)/(2)mv^(2)(1+(K^(2))/(R^(2)))`
`g xx (3v^(2))/(4g)=(1)/(2)v^(2)(1+(K^(2))/(R^(2)))`
`(3)/(2)=1+(K^(2))/(R^(2))`
`therefore (K^(2))/(R^(2))=(3)/(2)-1=(1)/(2)`
The value of `(K^(2))/(R^(2))` is `(1)/(2)` for disc.