If a bomb is thrown at a certain angle with the horizontal and after exploding on the way the different fragments move in different directions,then the centre of mass

$A$ mass $m$ is at rest on an inclined plane of mass $M$,which is further resting on a smooth horizontal plane. Now,if the mass $m$ starts moving under gravity,the position of the centre of mass of the system will

Two men,of masses $60 \, kg$ and $80 \, kg$,are sitting at the ends of a boat of mass $60 \, kg$ and length $4 \, m$. The boat is stationary. If the men now exchange their positions,then:

Two particles of masses $2 \ kg$ and $1 \ kg$ are moving along the same line with speeds of $2 \ m/s$ and $5 \ m/s$ respectively. If both particles are moving in the same direction,the speed of the centre of mass is $v_1$. If both particles are moving in opposite directions,the speed of the centre of mass is $v_2$. Find $v_1$ and $v_2$.

Two bodies of masses $m_1$ and $m_2$ are connected by a massless string passing over a massless,frictionless pulley as shown in the figure. Given $m_2 < m_1$. The acceleration of the center of mass of the system is:

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed