A uniform wire (Young's modulus 2 10¹¹ Nm ⁻² ) is subjected to longitudinal tensile stress of 5 10^7 Nm ⁻² . If the overall volume change in the wire is 0.02 % , the fractional decrease in the radius of the wire is close to:

Step-by-step solution

Given, y=2 10¹¹ Nm ⁻² aligned & Stress ( F A )=5 10^7 Nm ⁻² & V =0.02 %=2 10⁻⁴ ~m ^3 & r r =? aligned aligned & = stress strain strain ( ₀ )= stress & V =2 r ₀ r - r ^2 aligned From eqns (i) and (ii) putting the value of , ₀ and V and solving we get r r =0.25 10⁻⁴