Question

If a spring of stiffness $'k'$ is cut into two parts $'A'$ and $'B'$ of length $\ell_A : \ell_B = 2 : 3$, then the stiffness of spring $'A'$ is given by :

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

Answer 1

Answer: (D)

$\frac{5}{3k}$

Answer 2

$\ell_{A} = \frac{2\ell}{5},\,\,\ell_{B} = \left(\frac{3\ell }{5}\right)$ $K_{\ell} = K_{A}\ell_{A} = K_{B}\ell_{B}$ $K\ell = K_{A} \left(\frac{2\ell}{5}\right)$ $K_{A} = \frac{5K}{2}\quad\quad\quad\Rightarrow\quad K_{B} = \frac{5K}{3}.$