Two particles of equal mass $(m)$ each move in a circle of radius $(r)$ under the action of their mutual gravitational attraction. Find the speed of each particle.

$A$ star $2.5$ times the mass of the sun and collapsed to a size of $12 \;km$ rotates with a speed of $1.2 \;rev/s$. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity? (Mass of the sun $= 2 \times 10^{30} \;kg$)

Particles of mass $100 \, g$ each are placed at the vertices of an equilateral triangle of side $20 \, cm$. How much work must be done to increase the separation between them to infinity?

$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be:

For a satellite to orbit around the earth,which of the following must be true?

In the following four periods:
$(i)$ Time of revolution of a satellite just above the earth's surface $({T_{st}})$
$(ii)$ Period of oscillation of mass inside the tunnel bored along the diameter of the earth $({T_{ma}})$
$(iii)$ Period of simple pendulum having a length equal to the earth's radius in a uniform field of $9.8 \; N/kg \; ({T_{sp}})$
$(iv)$ Period of an infinite length simple pendulum in the earth's real gravitational field $({T_{is}})$