A pendulum comprising a light string of length `L` and small sphere, swings in the vertical plane . The string hits a peg located a distance of bellow the point of suspension (figure). If the pendulum is released from rest at the horizontal possition `(theta = 90^(@))` and is to swing in a complete circle centered on the peg, the minimum value of `d` is

Options

A. `0.75 m`
B. `0.5 m`
C. `0.25 m`
D. `0.2 m`

Answer

A

Explanation

Critical velocity at highest point `= sqrt (gl)` conservationof energy of the starting point and at the highest point implies
`:. Mgh = mg 2l + (1)/(2) mv^(2)`
`= mg 2l+ (1)/(2) mlg = mgl`
`h = (5)/(2)l = 1.25 m`