A sphere of radius 0 . 1   m and mass 8 π  kg is attached to the lower end of a steel wire of length 5 . 0   m & diameter 10 - 3   m . The wire is suspended from 5 . 22   m high ceiling of a room. When the sphere is made to swing like a simple pendulum, it just grazes the floor at its lowest point. Calculate the velocity of the sphere at the lowest position. Y for steel = 1 . 994 ×

Step-by-step solution

As the length of the wire is 5   m and diameter 2 × 0 . 1 = 0 . 2   m and at the lowest point, it grazes the floor which is at a distance 5 . 22   m from the roof, the increase in the length of the wire at lowest point Δ L = 5 . 2 2 - 5 + 0 . 2 = 0 . 0 2  m So the tension in the wire (due to elasticity) T = Y A L Δ L = 1 . 9 9 4 × 1 0 1 1 × π 5 × 1 0 - 4 2 × 0 . 0 2 5 = 1 9 9 . 4 π   N and as the equation of circular - motion of a mass m tied to