If an explosion occurs in a projectile,which force acts on its centre of mass?

If $M_2 = 2M_1$ and $\theta = 30^\circ$,the acceleration of $M_2$ is $a$. If the positions of the blocks are interchanged,what will be the acceleration of $M_2$?

$A$ uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is $0.5$. If the cylinder is $4\, cm$ in diameter and $10\, cm$ in height,which of the following is the minimum acceleration of the cart needed to cause the cylinder to tip over? (Assume $g = 10\, m/s^2$)

$A$ system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction $= \mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (Assume $m_1 = m_2 = m_3 = m$)

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,and if $a_{min}$ and $a_{max}$ are the minimum and maximum values of $a_0$ for which the blocks remain stationary with respect to the surface,then identify the correct statements.

Two carts are pushed apart by the explosion of a charge placed between them. $A$ cart of mass $100 \ kg$ stops after traveling a distance of $18 \ m$. What distance will a cart of mass $300 \ kg$ travel before stopping? The coefficient of friction $\mu$ between the carts and the ground is the same for both.