According to the Hooke's law the force required to change the length of a wire by $l$ is proportional to

According to the Hooke's law the force required to change the length of a wire by $l$ is proportional to
  1. $I^{-2}$
  2. $I^{-1}$
  3. $/$
  4. $I^2$

Solution

Given, change in length, $\Delta l=l$ $L=$ original length (say) According to Hooke's law, $ \begin{aligned} & \text { Stress } \propto \text { Strain } \\ & \Rightarrow \quad \frac{\text { Stress }}{\text { Strain }}=\text { constant } \\ & \Rightarrow \quad \frac{\text { Stress }}{\text { Strain }}=\text { Young's modulus } \\ & \Rightarrow \quad \frac{F / A}{\frac{\Delta l}{L}}=Y \quad \Rightarrow \quad \frac{F L}{A \Delta l}=Y \\ & F=\frac{Y \cdot A \Delta l}{L} \\ & \end{aligned} $ Since, $Y, A, L$ are constant. Hence, $\quad F \propto \Delta l$ But $\quad \Delta l=l$ $\therefore \quad F \propto l$

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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