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Combination of Springs

Two springs a...

Question

Two springs are in a series combination and are attached to a block of mass $m$ which is in equilibrium. The spring constants and the extensions in the springs are as shown in the figure. Then the force exerted by the spring on the block is:

\frac{k_{1} k_{2}}{k_{1} + k_{2}} (x_{1} + x_{2})

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k_{1} x_{1} + k_{2} x_{2}

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k_{1} x_{1}

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none of these

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Solution

The correct option is A $\frac{k_{1} k_{2}}{k_{1} + k_{2}} (x_{1} + x_{2})$
The equivalent force constant of the system is given as
$\frac{1}{k} = \frac{1}{k_{1}} + \frac{1}{k_{2}}$
$k = \frac{k_{1} k_{2}}{k_{1} + k_{2}}$
Total extension in the equivalent spring $= x = x_{1} + x_{2}$
Force in the equivalent spring = $F = k x$ $= \frac{k_{1} k_{2}}{k_{1} + k_{2}} (x_{1} + x_{2})$

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Two springs are in a series combination and are attached to a block of mass m which is in equilibrium. The spring constants and the extensions in the springs are as shown in the figure. Then the force exerted by the spring on the block is:

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