A smooth vertical rod is released from rest such that it is constrained to move vertically on a smooth wedge `(theta = 45^@)`. When the wedge moves through a distance `x`, the speed of the rod is :
.

Options

A. `sqrt(2gx)`
B. `sqrt((gx)/(2))`
C. `sqrt(gx)`
D. none of these

Answer

C

Explanation

Contraint relation is
`x=y cot theta, theta = 45 , x =y, v_(w) =v_(R)`
`Delta U_(G) = Delta_(K_(1))+Delta K_(2) , mgx = (1)/(2) mv^(2)+(1)/(2) mv^(2)`
`v = sqrt(gx)`.