In the figure shown a solid sphere of mass 4kg and radius 0.25 m is placed on a rough surface. `(g=10ms^(2)`)
(a). Minimum coefficient of friction for pure rolling to take place,
(b). If `mugtmu_(min)` find linear acceleration of sphere.
(c). if `mu=(mu_(min))/(2)`, find the linear acceleration of cylinder.
Here `mu_(min)` is the value obtained part (a).

Explanation

(a). `mu_(min)=(tantheta)/(1+(mR^(2)//I))`
`=(tan30^(@))/(1+5//2)=(2)/(7sqrt(3))`
(b). `a=(gsintheta)/(1+I//mR^(2))`
`=((10)sin30^(@))/(1+2//5)`
`=(25)/(7)m//s^(2)`
(c) `a=gsintheta-mugcostheta`
`=(10)sin30^(@)-((1)/(7sqrt(3)))(10)(cos30^(@))`
`=5-(5)/(7)=(30)/(7)m//s^(2)`