A thin horizontal disc is rotating about a vertical axis passing through its fixed centre $O$. Its angular momentum is $L_A$ and $L_B$ computed about points $A$ and $B$, respectively, with $O B=2 \times O A$. The value of $\frac{L_A}{L_B}$ is:

A solid sphere $A$ of radius $R$ and mass $M$ is attached at a point to a smaller solid sphere $B$ of radius $r

The angular speed of a flywheel is increased from 600 rpm to 1200 rpm in 10 s . The number of revolutions completed by the flywheel during this time is:

A thin wire of length ' $L$ ' and linear mass density ' $m$ ' is bent into a circular ring (in $x-y$ plane) with centre ' $C$ ' as shown in figure. The moment of inertia of the ring about an axis $y y^{\prime}$ will be: