Two wires A and B are of same material. Their lengths are in the ratio 1:2 and diameters are in the ratio 2:1. When stretched by forces F_(A)andF_(B) respectively, they get equal increase in their lengths. Then the ratio F_(A)//F_(B) should be:

Two wires A and B are of same material. Their lengths are in the ratio

1.	Two wires A and B are of same material. Their lengths are in the ratio 1:2 and diameters are in the ratio 2:1. When stretched by forces F_(A)andF_(B) respectively, they get equal increase in their lengths. Then the ratio F_(A)//F_(B) should be:
Answer» `1:1` `1:2` `8:1` `2:1` Solution :As both wires of same material `Y_(A)=Y_(B)` `(F_A)/(pi(r_A)^(2)).(l_A)/(Deltal_A)=(F_B)/(pi(r_B)^(2)).(l_B)/(Deltal_B)` But,`Deltal_(A)=Deltal_(B)` `rArr(F_A)/(F_B)=(I_B)/(I_A).((r_A)/(r_B))^(2)=(2)/(1)((2)/(1))^(2)` `=8:1`