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

Options

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

Answer

D

Explanation

Velocity, `v=sqrt((2gh)/(1+K^(2)//R^(2)))`
Given, `h=(3v^(2))/(4g)`
`v^(2)=(2gh)/(1+(K^(2))/(R^(2)))=(2g 3v^(2))/(4g(1+(K^(2))/(R^(2))))=(6 gv^(2))/(4g(1+(K^(2))/(R^(2))))`
`1=(3)/(2(1+(K^(2))/(R^(2))))or 1+(K^(2))/(R^(2))=(3)/(2)or (K^(2))/(R^(2))=(3)/(2)-1=(1)/(2)`
`K^(2)=(1)/(2)R^(2)` (Equation of disc)
Hence, the object is disc.