A metal wire with circular cross section and length one metre is pulled with tensile force of 1000 ~N on each side. For the wire to be stretched not more than 0.25 ~cm , the minimum diameter of the wire required is (Young's modulus of the metal =10¹¹ ~Pa , take =1.77 )

Step-by-step solution

Tensile force, F =1000 ~N Length, L=1 ~m Change in length, L =0.25 10⁻² ~m Young modulus of the metal, Y=10¹¹ pa aligned & Y = stress Strain = FL A L & r ^2= FL Y L & = 1000 1 10¹¹ 0.25 10⁻² 3.14 = 1 25 10^4 aligned r= 1 5 10^2 1.77 Diameter, d =2 r = 2 5 1.77 10⁻²=2.26 ~mm