Two identical particles of mass $1 \, kg$ each go round a circle of radius $R$,under the action of their mutual gravitational attraction. The angular speed of each particle is:

During the motion of a planet from perihelion to aphelion,the work done by the gravitational force of the sun on it is ...........

$A$ uniform sphere $A$ with radius $R$ exerts a gravitational force $F$ on a small particle $B$ situated at a distance $2R$ from the centre of the sphere. $A$ spherical portion of diameter $R$ is cut from the sphere $A$ such that its centre lies on the line connecting the centre of sphere $A$ and particle $B$. If $F^{\prime}$ is the new gravitational force between the remaining part of the sphere $A$ and the particle $B$, then find the correct relation between $F$ and $F^{\prime}$.

$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a.$ The magnitude of the gravitational potential at a point situated at $a/2$ distance from the centre,will be

$Assertion$: Space rockets are usually launched in the equatorial line from west to east.
$Reason$: The acceleration due to gravity is minimum at the equator.

$A$ particle of mass $M$ is at a distance $a$ from the surface of a thin spherical shell of equal mass $M$ and radius $a$. Which of the following statements is correct regarding the gravitational field and potential inside the shell?