Question

A copper wire of negligible mass, length 1 m and cross-sectional area 10^–6 m² is kept on a smooth horizontal table with one end fixed. A ball of mass 1 kg is attached to the other end. The wire and the ball are rotating with an angular velocity of 20 rad/s. If the elongation in the wire is 10^–3 m, obtain the Young’s modulus of copper. If on increasing the angular velocity to 100 rad/s, the wire breaks down, obtain the breaking stress. 

Answer 1

The stretching force developed in the wire due to rotation of the ball is

F = mrω² = 1 × 1 × (20)² = 400 N

Stress in the wire = F/A = 400/10^-6 N/m²

Strain in the wire = 10^-3/1 = 10^-3

Young’s modulus, Y =  Stress/Strain = 400/10^-6 x 10^-3

= 4 × 10¹¹ N/m² 

Breaking stress = 1 x 1 x(100)²/10^-6 = 1010 N/m².