The radii and Young's moduli of two uniform wires A and B are in the ratio 2: 1 and 1: 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire A is one percent, the percentage increase in length of the wire B is

Step-by-step solution

Increase in length, l= F l A Y or l= F l r^2 y Percent increase in length, x= l l 100= F r^2 y Here, same longitudinal force is applied. So, aligned & x₁ x₂ = ( r₂ r₁ )^2 ( y₂ y₁ ) & 1 x₂ = ( 1 2 )^2 ( 2 1 )= 1 4 2 1 & 1 x₂ = 1 2 & x₂=1 2=2 % aligned