Question

Assertion Two springs of force constants $k_{1}$ and $k_{2}$ are stretched by the same force. If $k_{1}>k_{2}$, then work done in stretching the first $\left(W_{1}\right)$ is less than work done in stretching the second $\left(W_{2}\right)$.
Reason $F =k_{1} x_{1}=k_{2} x_{2} $
$ \frac{x_{1}}{x_{2}}=\frac{k_{2}}{k_{1}} $
$ \frac{W_{1}}{W_{2}}=\frac{\frac{1}{2} k_{1} x_{1}^{2}}{\frac{1}{2} k_{2} x_{2}^{2}}=\frac{k_{1}}{k_{2}}\left(\frac{k_{2}}{k_{1}}\right)^{2}=\frac{k_{2}}{k_{1}} $
As $k_{1} > k_{2}, W_{1} < W_{2}$

• A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion
• B. If both Assertion and Reason are true but Reason is not correct explanation of the Assertion
• C. If Assertion is true but Reason is false
• D. If Assertion is false but the Reason is true

Answer 1

Answer: (A)

As force $=k x$
Greater the $k$ greater will be force for constant $x$.