Question

Two closed coil springs of stiffness k and 2k are arranged in series in one case and in parallel in the other case. The ratio of stiffness of springs connected in series to parallel is

• A. $\frac{1}{3}$
• B. $\frac{1}{9}$
• C. $\frac{2}{3}$
• D. $\frac{2}{9}$

Answer 1

The correct option is D $\frac{2}{9}$

For series connection,

$k_e=\frac{k\times 2k}{k+3k}=\frac{2}{3}k$

For parallel connection,

$k_e^{\prime }=k+2k=3k$

$\therefore \frac{k_e}{k_e^{\prime }}=\frac{2k/3}{3k}=\frac{2}{9}$