A small solid cylinder of radius `r` is released coaxially from point A inside the fixed large cylindrical bawl of radius R as shown in figure. If the friction between the small and the large cylinder is sufficient enough to prevent any slipping then find.
(a). What fractions of the total energy are translational and rotational when the small cylinder reaches the bottom of the larger one?
(b). The normal force exerted by the small cylinder on the larger one when it is at the bottom.

Explanation

(a). `K_("trans")=(1)/(2)mv^(2)`
`K_(rot)=(1)/(2)Iomega^(2)=(1)/(2)((1)/(2)mr^(2))((v)/(r))^(2)=(1)/(4)mv^(2)`
`K=K_("trans")+K_(rot)=(3)/(4)mv^(2)`
`therefore(K_("trans"))/(K)=(2)/(3)implies(K_(rot))/(K)=(1)/(3)`
(b). From conservation of energy
`mg(R-r)=(3)/(4)mv^(2) `
`therefore(mv^(2))/(R-r)=(4)/(3)mg`
Now, `N-mg=(mv^(2))/(R-r)=` centripetal for `=(4)/(3)mg`
`thereforeN=(7)/(3)mg`