Two wires of the same material and same length but diameters in the ratio (1 : 2) are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio .........

Two wires of the same material and same length but diameters in the ra

1.	Two wires of the same material and same length but diameters in the ratio (1 : 2) are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio .........
Answer» `1:2` `4:1` `1:1` `16:1` Solution :The potential energy per unit volume `u = 1/2 (("stress") ^(2))/( " Young.s modulus") = (S ^(2))/( 2 Y) ""...(1)` In stress `S = F/A, F` is CONSTANT `therefore S prop (1)/(A)` `therefore (S_(1))/( S _(2)) = (A_(2))/( A _(1)) = (pi D _(2) ^(2))/( pi D _(1) ^(2)) = ((D _(2))/( D _(1)) ) ^(1) ""...(2)` Both the wires are of same MATERIAL so their Young.s modulus is ALSO same So from equation (1) `u prop S ^(2)` `(u _(1))/( u _(2)) = ((S _(1))/( S _(2)) ) ^(2)` ` = ((D _(2))/( D _(!))) ^(4)` (From equation (2)) `= ((2)/(1)) ^(4) = (16)/(1)` `therefore u _(1) : u _(2) =16:1`