Question

If a spring of stiffness ${}^{\prime }{K}^{\prime }$ is cut into two parts ${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ of length $l_A=l_B=2:3$, then the stiffness of spring ${}^{\prime }{A}^{\prime }$ is given by:

• A. $\frac{3K}{2}$
• B. $\frac{2K}{5}$
• C. $K$
• D. $\frac{5K}{2}$

Answer 1

The correct option is D $\frac{5K}{2}$

Let us suppose that the spring constant of $l_a$ is $K_1$ and that of $l_2$ is $K_2$.
Resultant spring constant = $K$.We know that
$\frac{1}{K}=\frac{1}{K_1}+\frac{1}{K_2}$
$⟹K<K_1$ and $K<K_2$
$\therefore$ Only (d) is possible as in this option $K_1>K$ (i.e $\frac{5K}{2}$)