Two wires A and B are made of same material having ratio of lengths L_A L_B = 1 3 and their diameters ratio d_A d_B =2 . If both the wires are stretched using same force, what would be the ratio of their respective elongations?

Step-by-step solution

L _ A L _ B = 1 3 and d _ A d _ B =2 L _ A = F _ A L _ A A _ A Y _ A and L _ B = F _ B L _ B A _ B Y _ B Given, F_A=F_B and Y_A=Y_B L _ A L _ B = F _ A L _ A A _ A Y _ A F _ B L _ B A _ B Y _ B = ( L _ A L _ B ) ( A _ B A _ A ) L _ A L _ B = ( L _ A L _ B ) ( 4 ~d _ B ^2 4 ~d _ A ^2 )= ( L _ A L _ B ) ( d _ B d _ A )^2 L _ A L _ B = ( 1 3 ) ( 1 2 )^2= 1 12