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Questions  

An imperfectly rough sphere moves from rest down a plane inclined at an angle α to the horizontal. The coefficient of friction between the inclined plane and sphere is μ.Then

a
if μ <  27  tan α,μ > 17  tan α,  then pure rolling is not possible.
b
if μ >  17  tan α,   then only pure rolling takes place.
c
if  μ >  27  tan α, then pure rolling takes place.
d
all of the above are wrong.

detailed solution

Correct option is C

For pure rolling μ≥  tanα/ 1+mr2Ic For solid sphere,IC=25  mr2 ∴μ≥tanα/1+52⇒μ≥27tanα⇒μmin=27tanα

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