A block sides down a smooth inclined plane when released from the top, while another falls freely from the same point. Which one of them will strike the ground : (a) earlier (b) with greater speed ?

Explanation

In case of sliding motion on the inclined plane.
`" "(h)/(s) = sin theta rArr s = (h)/(sin theta), a = g sin theta`
`" "t_s = sqrt((2s)/(a)) = sqrt((2)/(g sin theta)xx (h)/(sin theta)) = (1)/(sin theta) sqrt((2h)/(g))= (t_F)/(sin theta)`
`v_s = sqrt ( 2as) = sqrt(2 g sin theta xx (h)/(sin theta)) = sqrt(2 gh)`

In case of free fall `t_F = sqrt((2h)/(g)) and v_F = sqrt(2gh) = v_s`
(a) `because sin theta lt 1, t_F lt t_s`, i.e., falling body reaches the ground first.
(b) `v_F= v_s` i.e., both reach the ground with same speed.
Special Note : (not same velocity, as for falling body direction is vertical while for sliding body along the plane downloads).