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