A small sphere of mass `m` and radius `r` is placed inside a horizontal hollow cylinder of radius `R`. Now cylinder rotating with some angular acceleration which slowly increases from zero to certain value `alpha`.

Options

A. Maximum angle `theta` formed by line joining centre will be `theta=sin^(-1)((2alphaR)/(5g))`
B. Angular velocity of sphere will be `omega^(')=(omegar)/R` where `omega` is angular velocity of cylinder
C. Sphere will keep rotating at lowest position
D. K.E. of sphere becomes constant when it reaches maximum height

Answer

A

Explanation

Acceleration slowly increases from zero to`alpha`, so small sphere will be rest w.r.t ground when maximum acceleration `alpha` is to be reached in framed of cylinder, small sphere will have `alphar=(gsintheta+alphar)/(1+2/5)`
`7/5 alphar-alphar=gsintheta`
`theta=sin^(-1)((2alphar)/(5g))`