$A$ spring has length $l$ and force constant $K$. If 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 $l_2$ is

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.)

Two massless springs of spring constant $K_1$ and $K_2$ are connected in series,suspended vertically,and a certain mass is attached to the free end. If $e_1$ and $e_2$ are their respective extensions and $f$ is the stretching force,the total extension produced 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

$A$ spring whose unstretched length is $\ell$ has a force constant $k$. The spring is cut into two pieces of unstretched lengths $\ell_1$ and $\ell_2$ where $\ell_1 = n\ell_2$ and $n$ is an integer. The ratio $k_1/k_2$ of the corresponding force constants $k_1$ and $k_2$ will be:

Assertion $(A)$: When a spring is cut into two equal parts,the spring constant of each piece is twice that of the original spring. Reason $(R)$: Spring constant is inversely proportional to the length of the spring.