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.s modulus `y=F/(A Deltal)` but `V=Al rArr l=V/A`
`therefore y=(FV)/(A^2Deltal)`
`therefore F=(yA^2 Al)/V`, y , `Deltal` and V constant
`therefore F prop A^2`
`therefore F_2/F_1=(A_2/A_1)^2 = ((3A)/A)^2=9`
`therefore F_2=9F " " [ because F_1=F]`