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:

$A$ spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released,the spring exerts an equal and opposite force on each cart for the same time $t$. If the coefficient of friction $\mu$ between the ground and the carts is the same,find the ratio of the displacements of the two toy carts.

$A$ $2 \, kg$ mass starts from rest on a smooth inclined surface with an inclination of $30^\circ$ and a length of $2 \, m$. What distance $S$ (in meters) will it travel before coming to rest on a rough horizontal surface with a coefficient of friction of $0.25$?

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. The surface under $M$ is smooth,while the vertical surface under $m$ is rough with a coefficient of friction $\mu$. The minimum value of $\mu$ for which the block $m$ remains stationary is:

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The tension in the string when it is vertical is:

Find the accelerations $a_1, a_2$ and $a_3$ of the blocks if a $10\,N$ force $F$ is applied on the $3\,kg$ block as shown in the figure.