Consider the situation as shown in the figure. A solid sphere of mass `m` is released from rest from the rim of a hemispherical cup so that it rolls along the surface. Find the normal contact force between the solid sphere and the cup at the bottom most point.

Explanation

Applying the energy conservation between `A` and `B`.
`K_(A)+U_(A)=K_(B)+U_(B)`
`0+mgR=(1)/(2)mv^(2)(1+(k^(2))/(R^(2)))+0`
`=(1)/(2)mv^(2)(1+(2)/(5))[since (k^(2))/(R^(2))=(2)/(5)]`
`mv^(2)=(10)/(7)mgR`
`N-mg=(mv^(2))/(R)=(10)/(7)mg`
`N=(17)/(7)mg`