A small body of mass m slide without friction from the top of a hemispherical cup of radius r as shown in figure. If leaves the surface to the cup at vertial distance h below the highest point then

Options

A. `h=r`
B. `h=r//2`
C. `h=r//3`
D. `2r//3`

Answer

C

Explanation

From figure,

`g cos theta =(v^(2))/(r)`
`v^(2)= g r cos theta `
`cos theta =(r-h)/(r)`
`therefore v^(2)=g r((r-h))/(r) =g(r-h)`...…(i)
By third kinematical equation of motion
`v^(2)=2 gh` ........(ii)
From equation (i) and (ii)
` g(r-h)=2gh`
` therefore h=(r)/(3)`