question_answer

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- sectional area 3A. If the length of wire 1 increases by\[\Delta x\]on applying force F, how much force is needed to stretch wire 2 by the same amount?                                                                                 [AIEEE 2009]

A)  F                    

B)       4F

C)  6F                   

D)       9F

Correct Answer: D Solution : [d] \[{{\ell }_{1}}=3{{\ell }_{2}}\]

\[Y=\frac{F}{A}\times \frac{{{\ell }_{1}}}{\Delta x}\]                 (i)

\[Y=\frac{F'}{3A}\times \frac{{{\ell }_{1}}/3}{\Delta x}\] (ii)

\[\frac{F}{A}\times \frac{{{\ell }_{1}}}{\Delta x}=\frac{F'}{3A}\times \frac{{{\ell }_{1}}}{3\Delta x}\]

\[F'=9F\]