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)

$k_1{x}_1=k_2{x}_2=F<br/>W_1=\frac{1}{2}{k}_1{x}_1^2=\frac{{\left(k_1{x}_1\right)}^2}{2k_1}=\frac{F^2}{2k_1}$
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.