Question

Two closed coil springs of stiffness s and 2s are arranged in series in one case and in parallel in other case. The ratio of stiffness of springs connected in series to parallel is-
1. 1/6
2. 2/9
3. 2/3
4. 1/3

Answer 1

Correct Answer - Option 2 : 2/9

Concept:

When two springs of stiffness k1 and k2 are connected in series, the equivalent stiffness is given by –

\(\frac{1}{{{k_{eq}}}} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}}\)

When two springs of stiffness k1 and k2 are connected in parallel, the equivalent stiffness is given by:

keq = k1 + k2

Calculation:

Given:

k1 = s, k2 = 2s

When connected in series:

\(\frac{1}{{{k_{eq}}}} = \frac{1}{{{k_1}}} + \frac{1}{{{k_2}}}\)

\(\frac{1}{{{k_{eq}}}} = \frac{1}{{{s}}} + \frac{1}{{{2s}}}=\frac{3}{2s}\)

∴ keq = \(\frac{2s}{3}\).

When connected in parallel:

keq = k1 + k2 = 3s

∴ The ratio of stiffness of springs connected in series to parallel is 2/9