Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in the air,

$A$ man weighing $80\, kg$ is standing at the centre of a flat boat and he is $20\, m$ from the shore. He walks $8\, m$ on the boat towards the shore and then halts. The boat weighs $200\, kg$. How far is he from the shore at the end of this time?

$A$ cart of mass $M$ is tied to one end of a massless rope of length $10\, m$. The other end of the rope is held by a man of mass $M$. The entire system is on a smooth horizontal surface. The man is at $x = 0$ and the cart is at $x = 10\, m$. If the man pulls the cart by the rope,the man and the cart will meet at the point:

Two objects of masses $200 \ g$ and $500 \ g$ have velocities $10\hat{i} \ m/s$ and $3\hat{i} + 5\hat{j} \ m/s$ respectively. The velocity of their center of mass (in $m/s$) is:

$A$ man of mass $M$ stands at one end of a plank of length $L$ which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is $3M$,the distance that the man moves relative to the ground is:

If a gas is filled in a stationary sphere,its molecules are in random motion due to thermal energy. Will the center of mass of these molecules be in motion?