A circular disc reaches , from top to bottom , of an inclined plane of length S . When it slips down the plane , it takes time t_(1) . When it rolls down the plane , it takes t_2 . Calculate the ratio (t_(2))/(t_(1))

A circular disc reaches , from top to bottom , of an inclined plane of

1.	A circular disc reaches , from top to bottom , of an inclined plane of length S . When it slips down the plane , it takes time t_(1) . When it rolls down the plane , it takes t_2 . Calculate the ratio (t_(2))/(t_(1))
Answer» Solution :Time taken in rolling down = `SQRT(2S (1 + (K^2)/(R^2)))/(G sin theta)` For a disc, `K^2 = R^2//2 ,= 1 + (K^2)/(R^2) = (3)/(2)` `THEREFORE t_(2) = sqrt((2 S xx 3)/(g sin theta xx 2))` or `t_(2) = sqrt((3 S)/(g sin theta))` Time taken in SLIPPING down `t_1 = sqrt((2S)/(g sin theta))` `therefore (t_(2))/(t_(1)) = sqrt((3S)/(g sin theta) xx (g sin theta)/(2 S))` or `(t_(2))/(t_(1)) = sqrt((3)/(2))`