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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 $-2$ : $k_1 < k_2$.
Statement $-1$ is true, Statement $-2$ is true and Statement $-2$ is not the correct explanation of Statement $- 1$.
Statement $-1$ is false, Statement $-2$ is true
Statement $-1$ is true, Statement $-2$ is false
Statement $-1$ is true, Statement $-2$ is true and Statement $-2$ is the correct explanation of statement $-1$.
Solution
$\frac{1}{2} \mathrm{k}_{1} \mathrm{x}_{1}^{2}>\frac{1}{2} \mathrm{k}_{2} \mathrm{x}_{2}^{2}$ given force is same
$\mathrm{k}_{1} \mathrm{x}_{1}=\mathrm{k}_{2} \mathrm{x}_{2}$
$\Rightarrow x_{1}>x_{2}$
$\Rightarrow \mathrm{k}_{1}<\mathrm{k}_{2}$
