A nail is located below the point of suspensions of a simple pendlum of length .l.. The bob is released from horizontal position. If the bob loops a verticle circle with nail as centre, find the distance of nail from point of suspension.

Explanation

Form the principal of conservation of mechanical energy
PE at the horizontal position = KE at the lowest position. `mgl = (1)/(2) mv^(2)`
To loop the verticle circle, `v^(2) = 5gh (1-x)` where .x. is the distance of nail from point of suspension, and .v. is the velocity at lowest point of path
`(mgl=(1)/(2)m.5g(l-x)),l=(5)/(2)(l-x), " " x = 3l//5`