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A solid uniform sphere having a mass M ,...

A solid uniform sphere having a mass M , radius R , and moment of inertia of `(2)/(5)MR^(2)` rolls down a plane inclined at an angle `theta` to the horizontal starting from rest. The coefficient of static friction between the sphere and the plane is `mu`. Then

A

The sphere will always roll without slipping

B

The sphere will always slide

C

The sphere will roll without slipping only if `theta le "sin" (7 mu)/(2)`

D

The sphere will roll without slipping only if `theta le "tan"^(-1) (7mu)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`mu ge (tan theta)/(1+ (MR^(2))/(I)) rArr mu ge (tan theta)/(1+ (5)/(2)) rArr theta le tan^(-1) ((7 mu)/(2))`
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