Question

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement 1 : If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$
Statement 2 : $k_1 < k_2$

• A. Statement 1 is false, Statement 2 is true
• B. Statement 1 is true, Statement 2 is false
• C. Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for statement 1
• D. Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1

Answer 1

Answer: (A)

$k_{1}x_{1}=k_{2}x_{2}=F
W_{1}=\frac{1}{2}k_{1}\,x^{2}_{1}=\frac{\left(k_{1}x_{1}\right)^{2}}{2k_{1}}=\frac{F^{2}}{2k_{1}}$
Similarly $W_{2}=\frac{F^{2}}{2k_{2}} \,\Rightarrow \,W\,\propto \frac{1}{k}$
$W_{1} > W_{2}\,\Rightarrow \, k_{1} < k_{2}$ statement-2 is true.
Statement-1 $W_{1}=\frac{1}{2}\,k_{1}\,x^{2}$
$W_{2} > W_{1}$
Statement-1 is false.