Question

An infinite number of springs having force constants as K, 2K, 4K, 8K, .......$\infty$ respectively are connected in series; then equivalent spring constant is

• A. K
• B. 2K
• C. $\frac{K}{2}$
• D. $\infty$

Answer 1

Answer: (C)

$\frac{K}{2}$

For the springs connected in series

$\frac{1}{K_{eq}}=\frac{1}{K}+\frac{1}{2K}+\frac{1}{4K}+\frac{1}{8K}+......$

$\frac{1}{K_{eq}}=\frac{1}{K}(1+\frac{1}{2}+\frac{1}{4}+.....)$

$\frac{1}{K_{eq}}=\frac{1}{K}\left(\frac{1}{1-\frac{1}{2}}\right)$

$\frac{1}{K_{eq}}=\frac{1}{K}\left(2\right)$

$K_{eq}=\frac{K}{2}$