A block of mass `m` is pressed against a horizontal spring fixed at one end to compress the spring through `(L_0)//(2)`. The natural length of the spring is `L_0` and spring constant `k=(mg)//(L_0)`. When released, the block moves horizontally on smooth surface till it leaves the spring. At what horizontal distance from O it strikes the ground.

Explanation

Between (1) and (2)
`(1)/(2)k((L_0)/(2))^2=(1)/(2)mv^2`
`v^2=(kL_0^2)/(4m)=(mg)/(L_0)xx(L_0)/(4m)=(gL_0)/(4)`
A to B (projectile motion)
`y=(gx^2)/(2v^2)implies8L_0=(gx^2)/(2xx(gL_0)/(4))`
`x^2=4L_0^2impliesx=2L_0`