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Q.

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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a

the speed and time of descend will be same

b

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

c

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

d

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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