Two wires are made of the same material and have the same volume. However wire 1 has cross-section area A and wire 2 has cross-section area 3A. If length of wire 1 increased by

Options

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

Answer

C

Explanation

(c) `Y=(FL)/(ADeltaL)`
or `F=(YADeltaL)/(L)=(YA^(2)DeltaL)/(AL)=(YA^(2)DeltaL)/(V)=(YA^(2)Deltax)/(V)`
where , AL=V= volume of wire, Young modulus in the same as both the wires are made of same material. It is given that both the wires have same volume and same extension in length.
`therefore (F')/(F)=(A'^(2))/(A^(2))=((3A)^(2))/(A^(2))=9`
`F'=9F`