$A$ simple spring has length '$l$' and force constant '$K$'. It is cut into two springs of length '$l_1$' and '$l_2$' such that $l_1 = n l_2$ ($n$ is an integer). The force constant of the spring of length '$l_1$' is:

$A$ spring of force constant $k$ is cut into two pieces such that one piece is three times the length of the other. The longer piece will have a force constant of

Two light vertical springs with equal natural lengths and spring constants $k_1$ and $k_2$ are separated by a distance $l$. Their upper ends are fixed to the ceiling and their lower ends to the ends $A$ and $B$ of a light horizontal rod $AB$. $A$ vertical downwards force $F$ is applied at point $C$ on the rod. $AB$ will remain horizontal in equilibrium if the distance $AC$ is

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

The tension in the spring is