Two identical bodies A and B of equal masses have initial velocities $\overrightarrow{v_1}=4 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\overrightarrow{v_2}=4 \hat{j} \mathrm{~m} / \mathrm{s}$ respectively. The body A has acceleration $\overrightarrow{a_1}=6 \hat{i}+6 \hat{j} \mathrm{~m} / \mathrm{s}^2$ while the acceleration of the other body B is zero. The centre of mass of the two bodies moves in $\_\_\_\_$ path.

The position of center of mass of three masses $2 \mathrm{~kg}, 3 \mathrm{~kg}$ and 15 kg placed with respect to mid point $(p)$ of normal bisector, as shown in the figure is $\_\_\_\_$ .

Two blocks of masses 2 kg and 1 kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in 2 s is _______ m. (Take $g = 10 \; m/s^2$)

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio $2: 2: 3$. The two pieces of equal masses fly off perpendicular to each other with a speed of $18 \mathrm{~m} / \mathrm{s}$ each. The velocity of the heavier fragment is

$\_\_\_\_$ $\mathrm{m} / \mathrm{s}$.