A ball of mass `m` and radius `r` rolls inside a hemispherical shell of radius `R`. It is released from rest from point `A` as shown in figure. The angular velocity of centre of the ball in position `B` about the centre of the shell is.
.

Options

A. `2sqrt(g/(5(R-r)))`
B. `2sqrt(g/(7(R-r)))`
C. `sqrt((2g)/(5(R-r)))`
D. `sqrt((5g)/(2(R-r)))`

Answer

B

Explanation

`KE` of ball in position `B=mg(R-r)`
Here `m=`mass of ball.
Since it rolls without slipping the ratio rotational to translational kinetic energy will be `2/5`
`(K_(R))/(K_(T))=2/5`
`K_(T)=2/7mg(R-r), 1/2mv^(2)=2/7mg(R-r)`
`v=2/(sqrt(7))sqrt(g(R-r)), omega=v/(R-r) =2 sqrt(v/(7(R-r)))`