When the acceleration of the $5\ kg$ block is $2\ m/s^2$ as shown in the figure,what will be the acceleration of the $15\ kg$ block? (in $m/s^2$)

An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

The force required to stretch a spring varies with the distance as shown in the figure. If the experiment is performed with the above spring of half length,the line $OA$ will

Two blocks with masses $100 \text{ g}$ and $200 \text{ g}$ are attached to the ends of springs $A$ and $B$ as shown in the figure. The energy stored in spring $A$ is $E$. The energy stored in spring $B$, when the spring constants $k_{A}$ and $k_{B}$ of springs $A$ and $B$ respectively satisfy the relation $4k_{A} = 3k_{B}$, is:

In the setup shown,a $200\, N$ block is supported in equilibrium with the help of strings and a spring. At point $O$,the strings are knotted. The extension in the spring is $4\, cm$. The force constant of the spring is closest to ............ $N/m$ $[g = 10\, m/s^2]$.

When a weight is applied to a spring,it stretches by an amount $x$. What is the energy stored in it? ($T$ is the tension force developed in the spring and $k$ is the spring constant.)