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

Options

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

Answer

B

Explanation

`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)))`