The length of a spring is $\alpha$ when a force of $4\,N$ is applied on it and the length is $\beta$ when $5\,N$ force is applied. Then the length of the spring when $9\,N$ force is applied is

$A$ block of mass $2 \,kg$ is connected to an ideal spring and is placed on a smooth horizontal surface. The spring is pulled to move the block and at an instant, the speed of end $A$ of the spring and speed of the block were measured to be $6 \,m/s$ and $3 \,m/s$, respectively. At this moment, the potential energy stored in the spring is increasing at a rate of $15 \,J/s$. Find the acceleration of the block at this instant. (in $\,m/s^2$)

$A$ spring of force constant $k$ is cut into three equal pieces. If these three pieces are connected in parallel,the force constant of the combination will be

$A$ spring of force constant $15 \ N/m$ is cut into two pieces. If the ratio of their lengths is $1 : 3$, then the force constant of the smaller piece is . . . . . . $N/m$.

Give an example of a variable force. Write the formula for Hooke's law.

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 $\text{ ms}^{-2}$)