A small solid sphere of mass `m` and radius `r` starting from rest from the rim of a fixed hemispherical bowl of radius `R(gt gtr)` rolls inside it without sliding. The normal reaction exerted by the sphere on the hemisphere when it reaches the bottom of hemisphere is

Options

A. `(3//7)mg`
B. `(9//7)mg`
C. `(13//7)mg`
D. `(17//7)mg`

Explanation

At bottom total kinetic energy
`=` decrease in potential energy
`=mgR`
The ratio `(K_(R))/(K_(T))=(2)/(5)`
`thereforeK_(T)=(1)/(2)mv^(2)=(5)/(7)mgR`
`therefore(mv^(2))/(R)=(10)/(7)mg=N-mg`
`thereforeN=(17)/(7)mg`