Two satellites $A$ and $B$,having a ratio of masses $3 : 1$,are in circular orbits of radii $r$ and $4r$ respectively. Calculate the ratio of the total mechanical energy of $A$ and $B$.

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is

The magnitude of the projection of the vector $\vec{a} = 4\hat{i} - 3\hat{j} + 2\hat{k}$ on the line which makes equal angles with the coordinate axes is

$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction,the magnetic field at the centre of the double loop will be

Lactose is composed of ......... .

The resolving power of an astronomical telescope is $0.2\, sec$. If the central half portion of the objective lens is covered,the resolving power will be....$sec$