Figure shows a smooth track, a part of which is a circle of radius R. As block of mass m is pushed against a spring of spring constant k fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force mg when it reaches the point P, where the radius of the track is horizontal.

Answer

C

Explanation

Given, N=mg
As shown in the ure
`(mv^2)/R=mg`
`rarr v^2=gR`……i

Total energy at point A
`=energy at P
`1/2kx^2=1/2mv^2+mgR`
`x^2=(mgR+2mgR)/k`
[because `v^2=gR]`
`rarr x^2=3mgR/k`
`rarr x=sqrt(((3mgR))/k)`