one end of a spring of natural length ha and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h figure. Initially, the spring makes an angle of `37^0` with the vertical when the system is released from rest. find the speed of the ring when the spring becomes vertical.

Options

A. `(h)/(2)sqrt((k)/(m))`
B. `(h)/(4)sqrt((k)/(m))`
C. `(h)/(2)sqrt((k)/(2m))`
D. `(h)/(4)sqrt((k)/(2m))`

Answer

B

Explanation

`cos37^@=(h)/(h+x)implies(4)/(5)=(h)/(h+x)`
`4h+4x=5himpliesx=(h)/(4)`
`(1)/(2)kx^2=(1)/(2)mv^2`
`v=sqrt((k)/(m))x=(h)/(4)sqrt((k)/(m))`