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:

Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

$A$ ball of mass $1\, kg$ is thrown up with an initial speed of $4\, m/s$. $A$ second ball of mass $2\, kg$ is released from rest from some height as shown in the figure. Select the correct alternative.

Two particles $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of $A$ is $v$ and the speed of $B$ is $2v$, the speed of the centre of mass is

Two bodies of masses $2\,kg$ and $4\,kg$ are moving with velocities $2\,m/s$ and $10\,m/s$ respectively towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass,given that the bodies were at rest initially?

Two spherical objects have masses $M$ and $5M$ and radii $R$ and $2R$ respectively. They are released in free space with their centers at a distance of $12R$. If they attract each other only due to gravitational force,the distance traveled by the smaller object before collision is: (in $R$)