Two springs,$P$ and $Q$,of force constants $k_P$ and $k_Q$ (where $k_Q = k_P / 2$) are stretched by applying forces of equal magnitude. If the energy stored in $Q$ is $E$,then the energy stored in $P$ is:

When a body is suspended from a spring and released slowly,the extension in the spring is $x$. If the body is released suddenly,the extension in the spring is:

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:

Two blocks are connected by a spring. The combination is suspended,at rest,from a string attached to the ceiling,as shown in the figure. The string breaks suddenly. Immediately after the string breaks,what is the initial downward acceleration of the upper block of mass $2m$?

$A$ small block of mass $100\,g$ is tied to a spring of spring constant $7.5\,N/m$ and natural length $20\,cm$. The other end of the spring is fixed at a point $A$. If the block moves in a circular path on a smooth horizontal surface with a constant angular velocity of $5\,rad/s$ about point $A$,then the tension in the spring is $.........\,N$.

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