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 the 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-l : When stretched by the same amount, work done on $S_1$, will be more than that of $S_2$
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 of statement- 1
• D. Statement-1 is true, statement-2 is true, statement-2 is not the correct explanation of Statement-1

Answer 1

The correct option is A Statement-1 is false, statement-2 is true

$k_1{x}_1=k_2{x}_2=F$

$W_1=\frac{1}{2}k{x}_1^2=\frac{F^2}{2k_1}$

Similarly for $W_2=\frac{F^2}{2k_2}$

Since $W\propto \frac{1}{k}$

$W_1.W_2$ $\Rightarrow k_1<k_2$, Statement-2 is true.

From Statement-1, $W_2>W_1$, hence it is false.