Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are $v$ and $2v$ at any instant, then the speed of centre of mass of the system will be

A wheel of mass $10\,kg$ has a moment of inertia of $160\,kg-m^2$ about its own axis. The radius of gyration is ........ $m.$

In a gravity free space, a man of mass $M$ standing at a height $h$ above the floor, throws a ball of mass $m$ straight down with a speed $u$ . When the ball reaches the floor, the distance of the man above the floor will be

A cockroach of mass $\frac {M}{2}$ is start moving, with velocity $V$ on the circumference of a disc of mass $'M'$ and $'R',$ what will be angular velocity of disc?

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,J$ . ....... $J$ is its translational $K.E$

Three masses of $2\,kg$, $4\, kg$ and $4\, kg$ are placed at the three points $(1, 0, 0)$ $(1, 1, 0)$ and $(0, 1, 0)$ respectively. The position vector of its center of mass is