A uniform spring has an unstretched length $L$ and a force constant $k$. The spring is cut into two parts of unstretched lengths $l_1$ and $l_2$ such that $l_2=\eta l_2$, where $\mathrm{\eta }$ is an integer. The corresponding force constants are $k_1$ and $k_2$, then

• A

  force has to be kept same to find $k_1$ and $k_2$
• B

  $k_1=\frac{k\left(\eta +1\right)}{\eta }$ and $k_2=k\left(\eta -1\right)$
• C

  $k_1=\frac{k\left(\eta -1\right)}{\eta }$ and $k_2=k\left(\eta +1\right)$
• Correct answer
  D

  $k_1=\frac{k\left(\eta +1\right)}{\eta }$ and $k_2=k\left(\eta +1\right)$

Hence, the correct answer is option: 'D'.