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A solid sphere rolls down two different ...

A solid sphere rolls down two different inclined planes of the same height but of different inclinations

A

In both cases the speed and time of decent will be same

B

The speed will be same but time of descent will be different

C

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

D

Speed and time of descend both will be different

Text Solution

Verified by Experts

The correct Answer is:
B
`a = (g sin theta)/(1+ k^(2)//r^(2))`, length of the track `=h/(sin theta) rArr h/(sin theta) =1/2. (g sin theta)/(1+k^(2)//R^(2)) t^(2) rArr t=sqrt((2h(1+k^(2) //R^(2)))/(q sin^(2)theta)`
and `mgh = 1/2 mv^(2) (1+k^(2)//R^(2)) rArr v=sqrt((2gh)/(1+k^(2)//R^(2)))`
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