Question

A sphere of radius 0.1 m and mass 8 pi kg is attached to the lower end of a steel wire of length 5 m and diameter 10^-3 m. The wire is suspended from 5.22 m high ceiling of a room. When the sphere is made to swing as a simple pendulum, it just grazes the floor at its lowest point. Calculate the velocity of the sphere at the lowest position . Young's modulus of steel is 1.994 x 10¹¹ N/m²

Answer 1

Let Δl be the extension of wire when the sphere is at mean position . Then we have

Let T be the tension in the wire at mean position during oscillations, then

Substituting the values, we have

The equation of motion at mean position is,

Substituting the proper values in Eq. (i) , we have