Sol. Take the mass m as a point mass. At the instant when the pendulum collides with the nail, m has a velocity v = . The angular momentum of the mass with respect to the point at which the nail locates is conserved during the collision. Then the velocity of the mass is still v at the instant after the collision and the motion thereafter is such that the mass is constrained to rotate around the nail. Under the critical condition that the mass can just swing completely round in a circle, the gravitational force when the mass is at the top of the circle. Let the velocity of the mass at this instant be v 1 , and we have

= mg,

or v 1 2 = ( λ – d) g.

The energy equation

= ,

Or 2g λ = ( λ – d)g + 4( λ – d)g

then gives the minimum distance as d = .