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A sphere can roll on a surface inclined at an angle $θ$ if the friction coefficient is more than $\frac{1}{7} g \tan θ$ . If a sphere is released from rest on the incline

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it will make pure translational motion

the angular momentum of the sphere about its centre will remain constant

it will translate and rotate about the centre

it will stay at rest

answer is C.

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Detailed Solution

As the condition for minimum coefficient of friction is satisfied the sphere rolls down hence it has both translatory and rotatory motions

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