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(A) The spring constant $k$ is defined by Hooke's Law as $F = kx$,where $F$ is the applied force (load) and $x$ is the extension.From the graph,the ex

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$0.1$

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(A) The spring constant $k$ is defined by Hooke's Law as $F = kx$,where $F$ is the applied force (load) and $x$ is the extension.From the graph,the extension $x$ is zero when the load is $1 \, kg$. This indicates an initial offset.We consider the change in load $\Delta F$ and the corresponding change in extension $\Delta x$.At load $F_1 = 1 \, kg$,extension $x_1 = 0 \, cm$.At load $F_2 = 4 \, kg$,extension $x_2 = 30 \, cm$.Therefore,$\Delta F = F_2 - F_1 = 4 - 1 = 3 \, kg$.And $\Delta x = x_2 - x_1 = 30 - 0 = 30 \, cm$.The spring constant $k$ is the reciprocal of the slope of the extension versus load graph (or $k = \frac{\Delta F}{\Delta x}$):$k = \frac{3 \, kg}{30 \, cm} = 0.1 \, kg/cm$.

The pointer reading versus load graph for a spring balance is as given in the figure. The spring constant is ........ $kg/cm$.

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