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

If a spring is extended to length $l,$ then according to Hooke's law,

$A$ 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 . . . . . . $N/m$.

Two springs of force constants $K_1$ and $K_2$ are loaded with weights $W_1$ and $W_2$ respectively. Assume that the length of each spring is increased by the same amount. If $K_1 = 2 K_2$, then the ratio $\frac{W_2}{W_1}$ is

The spring extends by $x$ on loading,then the energy stored by the spring is: (if $T$ is the tension in the spring and $k$ is the spring constant)

$A$ spring of length $l$ has a force constant $k$. When a weight $W$ is attached to it,the extension produced is $x$. If the spring is cut into two equal parts and these parts are connected in parallel to support the same weight $W$,what will be the new extension?