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

What is the acceleration of $3 \,kg$ mass when the acceleration of $2 \,kg$ mass is $2 \,m/s^2$ as shown in the figure? (in $m/s^2$)

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 ............ $N/m$ $[g = 10\, m/s^2]$.

Two massless springs of spring constants $K_1$ and $K_2$ are connected in series, suspended vertically, and a mass is attached to the free end. If $x_1$ and $x_2$ are their respective extensions and $F$ is the stretching force, what is the total extension produced?

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

If a spring of stiffness $k$ is cut into two parts $A$ and $B$ of length $l_{A}: l_{B}=2: 3$,then the stiffness of spring $A$ is given by