In the $HCl$ molecule, the separation between the nuclei of the two atoms is about $1.27\,\mathop A\limits^o \left( {1\,\mathop A\limits^o  = {{10}^{ - 10}}\,m} \right)$. The approximate location of the centre of mass of the molecule from hydrogen atom, assuming the chlorine atom to be about $35.5$ times massive as hydrogen is ....... $\mathop A\limits^o $

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively, and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1=4$ then $\frac{{{r_2}}}{{{r_1}}}$ equals

$A$ car travelling on a smooth road passes through $a$ curved portion of the road in form of an arc of circle of radius $10 m$. If the mass of car is $500\, kg$, the reaction on car at lowest point $P$ where its speed is $20 m/s$ is ......... $kN$.

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to the disc and passing through the centre), and rotating with angular speed $\omega _1$ and $\omega _2$ are brought into contact face to face with their axes of rotation coincident. What is the loss in kinetic energy of the system in the process?

A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$ , which can slide freely along the rod. Initially the two beads are at the centre of the rod and the system is rotating with angular velocity $\omega _0$ about its axis perpendicular to the rod and passing through its mid-point (see figure). There are no external forces. When the beads reach the ends of the rod, the angular velocity of the system is

A tube of length $L$ is filled completely with an incompressible liquid of mass $M$ and closed at both ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega $ . Then the force exerted by the liquid at this other end is