Two particles whose masses are $10\,kg$ and $30\,kg$ and their position vectors are $\hat i +\hat j+ \hat k$ and $-\hat i -\hat j -\hat k$ respectively would have the centre of mass at

A force $\vec F$ acts on a particle having position vector $\vec r$ (with respect to origin). It produces a torque $\vec \tau $ about origin, choose the correct option

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

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same time $t$. The ratio of the angular speeds of the first to the second car is

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 ........ $m.$

A particle of mass $m$ moves in the $XY$ plane with a velocity $V$ along the straight line $AB$ . If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$ , then