The Young's modulus of brass and steel are 10 ^(11) Nm ^(-2) and 2 xx 10 ^(11) Nm ^(-2)respectively. A brass wire and a steel wire of the same length extend by 1 mm, each under the same force. If radii of brass and steel wires are R_(B) and R_(S) respectively, then .. .

The Young's modulus of brass and steel are 10 ^(11) Nm ^(-2) and 2 xx

1.	The Young's modulus of brass and steel are 10 ^(11) Nm ^(-2) and 2 xx 10 ^(11) Nm ^(-2)respectively. A brass wire and a steel wire of the same length extend by 1 mm, each under the same force. If radii of brass and steel wires are R_(B) and R_(S) respectively, then .. .
Answer» `R _(S) = (R _(B))/(sqrt2)` `R _(S) = (R _(B))/(2)` `R _(S) = sqrt2 R _(B)` `R _(S) = 4 R _(B)` SOLUTION :Young.s modulus `Y= ( F //A)/(DELTA L //L)` `therefore Y = (FL)/(A Delta L) = (FL )/(PI R ^(2) Delta L )` `therefore Y prop (1)/(R ^(2)) [because F,L, Delta L and pi` are constant] `therefore (Y_(S))/( Y_(B)) = ((R_(B))/(R _(S))) ^(2)` `therefore (2 xx 10 ^(11))/( 10 ^(11)) = ((R _(B))/( R _(S))) ^(2)` `therefore 2 = ((R _(B))/( R _(S)))^(2)` `therefore sqrt2 = (R _(B))/( R _(S))` `therefore R _(S) = (R _(B))/(sqrt2)`