$A$ long spring is stretched by $2 \ cm$ and its potential energy is $U$. If the spring is stretched by $10 \ cm$,its potential energy will be

$A$ 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 $.........\,N$.

The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now, the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

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

Initially,the spring is at its natural length and both blocks are at rest. Determine the maximum extension in the spring. Given $k = 20 \ N/m$,$m_1 = 0.5 \ kg$,$m_2 = 1 \ kg$,and $F = 1 \ N$.

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.)