A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In both cases

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the speed and time of descend will be same

the speed will be same but time of descend will be different

the speed will be different but time of descent will be same.

speed and time of descent both are different.

answer is B.

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Detailed Solution

Speed of the rolling body at the bottom of inclined plane isv = 2gh1+k2R2where h is height of the inclined plane, k and R be radius of gyration and radius of the body respectively.For solid sphere, k2R2 = 25v = 2gh1+25 = 107ghAs h is same in both the cases, therefore speed will be same in both cases.Time of descent, t = 1sinθ2hg(1+k2R2)Where θ is angle of inclination?For solid sphere, k2R2 = 25t = 1sinθ14 h5 gAs h is same but θ is different in both the cases, hence time of descend will be different in both the cases.

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