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Answer» Direction of friction is up the plane
Total mechanical energy of the sphere remains constant
Angular momentum of sphere remains conserved about instantaneous point of CONTACT
Solution :When sphere TRIES to slip down the plane DUE to component of its weight along the same plane then friction acts upon the plane to oppose the POSSIBLE relative motion at the contact. Friction acting this way provides necessary torque about the centre for rotational motion so that sphere may perform pure rolling. In case of pure rolling instantaneous velocity of the point of contact is zero and this is the point where friction acts hence work done by the friction remains zero and total mechanical energy remains conserved because there is no heat loss due to friction. Note that there is torque of weight of the sphere about point of contact hence angular momentum of the sphere about point of contact cannot remain constant. So options (a), (b) and (c) are CORRECT.
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