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).

In the figure shown a solid sphere of mass 4kg and radius 0.25 m is p

1.	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).
Answer» (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)`

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