$A$ spring has length $L$ and force constant $K$. It is cut into two springs of length $L_1$ and $L_2$ such that $L_1 = N L_2$ ($N$ is an integer). The force constant of the spring of length $L_1$ is:

$A$ body of mass $m$ is suspended from an ideal spring of force constant $k$. The expected change in the position of the body due to an additional force $F$ acting vertically downwards is

$A$ force of $20\,dyne$ applied to the end of a spring increases its length by $1\,mm$. What will be the force constant of the spring?

The figure shows two cases. In the first case,a spring (spring constant $K$) is pulled by two equal and opposite forces $F$ at both ends. In the second case,it is pulled by a force $F$ at one end while the other end is fixed. The extensions $(x)$ in the springs will be:

$A$ spring of force constant $k$ is cut into three equal parts. The force constant of each part would be

Find the acceleration of the $3 \text{ kg}$ mass when the acceleration of the $2 \text{ kg}$ mass is $2 \text{ ms}^{-2}$ as shown in the figure. (in $\text{ ms}^{-2}$)