question_answer

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 \[\Delta /\]on applying a force F, how much force is needed to stretch the second wire by the same amount?                 [NEET - 2018]

A) 4 F

B) 6 F

C) 9 F

D) F

Correct Answer: C

Solution :

[c]

For wire 1,

\[\Delta \text{l=}\left( \frac{\text{F}}{\text{AY}} \right)\text{3l}\]              (i)

For wire 2,

\[\frac{\text{F }\!\!'\!\!\text{ }}{3A}=Y\frac{\Delta \text{I}}{\text{I}}\]

\[\Rightarrow \]   \[\Delta I=\left( \frac{F'}{3AY} \right)I\] (ii)

From equation (i) & (ii),

\[\Delta \text{I=}\left( \frac{\text{F}}{\text{AY}} \right)\text{3I=}\left( \frac{\text{F }\!\!'\!\!\text{ }}{\text{3AY}} \right)\text{I}\]

\[\Rightarrow \]