Two wires A and B are of the same material their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, their increase in length will be in the ratio ........

Two wires A and B are of the same material their lengths are in the ra

1.	Two wires A and B are of the same material their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, their increase in length will be in the ratio ........
Answer» `2:1` `1:4` `1:8` `8:1` Solution :We know that Young.s modulus `Y = (F)/(pi r ^(2)) xx (L)/(l)` Here Y and FARE CONSTANTS for both wires. `THEREFORE (1)/( r _(1) ^(2)) . (L_(1))/( l _(1)) = ( 1)/( r _(2)^(6)). (L_(2))/( l _(2))` `therefore ( l _(1))/(l_(2)) = (r _(2) ^(2) xx L _(1))/( r _(1) ^(2) xx L _(2)) = (((D _(2))/( 2 )) ^(2) xx L _(1))/(( (D _(1))/( 2 )) ^(2) xx L _(2))` `therefore ( l _(1))/( l _(2)) = ( D _(2) ^(2) xx L _(1))/( D _(1) ^(2) xx L _(2)) = ( D _(2) ^(2))/( ( 2D _(2)) ^(2)) xx (L _(2))/( 2 L _(2)) = 1/8` HENCE `l _(1) : l_(2) = 1:8`