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.

A small sphere of mass m and radius r is placed inside a horizontal ho

1.	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.
Answer» Maximum angle `theta` formed by LINE joining centre will be `theta=sin^(-1)((2alphaR)/(5G))` Angular velocity of sphere will be `omega^(')=(omegar)/R` where `omega` is angular velocity of cylinder Sphere will KEEP rotating at lowest position K.E. of sphere becomes constant when it reaches maximum height Solution :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))`

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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.

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