Three different balls of masses `m_(1), m_(2)` and `m_(3)` are allowed to roll form rest on three firctionless parth OA, OB and OC respectively from O. The height of O above the ground is h. The respective speeds `S_(1), S_(2) and S_(3)` of `m_(1), m_(2), and m_(3)` at the bottom A, B and C are

Options

A. `(S_(1))/(m_(1)) (S_(2))/(m_(2)) = (S_(3))/(m_(3))`
B. `m_(1)S_(1)^2 = m_(2)S_(2)^2 = m_(3)S_(2)^3`
C. `S_(2) lt S_(1) lt S_(3)`
D. `S_(1) lt S_(2) lt S_(3)`

Answer

b

Explanation

Final speed depends only on the vertical displaceent-h is same. So `s_(1) = s_(2) = s_(3)`.