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 :

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