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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 $S_1$, Work done on $S_1$ is more than $S_2$
STATEMENT2: $k_1 < k_2$
Statement $1$ is true, Statement $2$ is true, Statement $2$ is not the correct explanation for 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, Statement $2$ is the correct explanation for Statement $1$
Solution
When force is same
$W = \frac{1}{2}\,k{x^2}$
$W = \frac{1}{2}k\frac{{{F^2}}}{{{k^2}}}\,\left[ {\because F = kx} \right]$
$\because $ W =$\frac{{{F^2}}}{{2x}}$
As ${W_1} > {W_2}$
$\therefore {k_1} < {k_2}$
When extension is same
W $ \propto $ k ($\because $ $x$ is same )
$\therefore $${W_1} < {W_2}$
statement $1$ is false and statement $2$ is teue.
