Two springs of spring constants $k_{1}$ and $k_{2}$ are joined in series. The effective spring constant of the combination is given by -

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

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k_{1} + k_{2}

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

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\sqrt{k_{1} k_{2}}

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Solution

The correct option is C $\frac{k_{1} k_{2}}{(k_{1} + k_{2})}$
Two springs of spring constant $k_{1}$ and $k_{2}$ are joined in series.
The effective spring constant of the combination is -
We know using hooke's law
$\frac{f_{1}}{k_{1}} = x_{1} \frac{f_{2}}{k_{2}} = x_{2} X = \frac{f_{1}}{k_{1}} + \frac{f_{2}}{k_{2}} X = \frac{F}{k_{1}} + \frac{F}{k_{2}} X = F (\frac{1}{k_{1}} + \frac{1}{k_{2}}) X = F [\frac{(k_{1} + k_{2})}{k_{1} k_{2}}] F = \frac{k_{1} k_{2}}{(k_{1} + k_{2})} X T h e r e f o r e, k = \frac{k_{1} k_{2}}{(k_{1} + k_{2})}$

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