Two wires are made of the same material and have the same volume. The first wire has cross sectional area A and the second wire has cross sectional area 3A. If the length of the first wire is increased by `Deltal` on applying a force F, how much force needed to stretch the second wire by the same amount ?

Options

A. F
B. 9F
C. 4F
D. 6F

Answer

B

Explanation

Young modulus `Y = ( Fl )/(A Delta l)`
but `V = Al implies l = (V)/(A)`
`therefore Y = (FV )/( A ^(2) Delta l )`
`therefore ` in ` F = ( YA ^(2) Delta l )/(V) Y, Delta l` and V are equal
`therefore F prop A ^(2)`
`therefore (F _(2))/(F _(1)) =((A _(2))/( A _(1))) ^(2)`
`= ((3 A )/( A )) ^(2) = 9`
`thereforeF _(2)=9F " "[because F _(1) = F]`