The force required to stretch a spring varies | vedclass

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(A) The force $F$ required to stretch a spring by a distance $x$ is given by $F = kx$,where $k$ is the spring constant.For a spring of length $L$,the

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Shift towards $F$-axis

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(A) The force $F$ required to stretch a spring by a distance $x$ is given by $F = kx$,where $k$ is the spring constant.For a spring of length $L$,the spring constant $k$ is inversely proportional to its length,i.e.,$k \propto \frac{1}{L}$.If the length of the spring is halved $(L' = L/2)$,the new spring constant $k'$ becomes $k' = k \cdot (L/L') = k \cdot (L / (L/2)) = 2k$.The slope of the force-displacement graph is equal to the spring constant $k$. Since the new spring constant $k'$ is double the original value,the slope of the line $OA$ increases.An increase in the slope of a line passing through the origin in an $F-x$ graph means the line shifts towards the $F$-axis.Therefore,the correct option is $A$.

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length,the line $OA$ will

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