$A$ particle of mass $m$ is thrown horizontally from the top of a tower and another particle of mass $2m$ is thrown vertically upward. The acceleration of the centre of mass is .............

As shown in the figure,two blocks are connected with a light spring. When the spring is at its natural length,velocities are given to them as shown in the figure. Choose the wrong alternative.

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,m$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

Four particles $A, B, C$ and $D$ with masses $m_A=m, m_B=2m, m_C=3m$ and $m_D=4m$ are at the corners of a square. They have accelerations of equal magnitude $a$ with directions as shown. The acceleration of the centre of mass of the particles is

$A$ $500\,kg$ boat is $9\,m$ long and is floating without motion on still water. $A$ man of mass $100\,kg$ is at one end and if he runs to the other end of the boat and stops,the displacement of the boat is

Two bodies of masses $2\ kg$ and $4\ kg$ are moving with velocities $2\ m/s$ and $10\ m/s$ respectively along the same direction. The velocity of their centre of mass will be ......... $m/s$.