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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. 

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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/m

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

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