If $K_{i}$ and $K_{p}$ respectively are effective spring constant in series and parallel combination of springs as shown in figure, find $\frac{K_{i}}{K_{p}}$

\frac{9}{2}

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\frac{3}{7}

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\frac{2}{9}

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\frac{7}{3}

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Solution

The correct option is C $\frac{2}{9}$
In a series combination of above springs, effective spring constant $K_{i} = \frac{K_{1} K_{2}}{K_{1} + K_{2}}$
$∴$ $K_{i} = \frac{K \times 2 K}{K + 2 K}$ $= \frac{2 K}{3}$
In parallel combination of above springs, effective spring constant $K_{p} = K_{1} + K_{2}$
$∴$ $K_{p} = K + 2 K = 3 K$
Thus $\frac{K_{i}}{K_{p}} = \frac{2 K / 3}{3 K} = \frac{2}{9}$

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