$A$ 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

$A$ 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:

Two blocks of mass $2 \, kg$ and $4 \, kg$ are accelerated with the same acceleration by a force of $10 \, N$ as shown in the figure on a smooth horizontal surface. Then the spring force between the two blocks will be .......... $N$ (the spring is massless).

The block $A$ is pushed towards the wall by a distance $x$ and released. The normal reaction $N$ by the vertical wall on the block $B$ versus the compression $x$ in the spring is given by:

Two masses of $10\, kg$ and $20\, kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant when the $10\, kg$ mass has an acceleration of $12\, m\, s^{-2}$,the acceleration of the $20\, kg$ mass is ...... $m\, s^{-2}$.

Initially,a spring is at its natural length. $A$ block of mass $2 \, kg$ is attached to the lower end,and a block of mass $0.25 \, kg$ is at the top. If the system is released from the position where the spring is at its natural length,find the maximum force exerted by the system on the floor? (in $N$,take $g = 10 \, m/s^2$)