Two point masses of mass $4m$ and $m$ respectively,separated by a distance $d$,are revolving under their mutual force of attraction. The ratio of their kinetic energies is:

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ are released in free space with initial separation between their centres equal to $12R.$ If they attract each other due to gravitational force only,then the distance covered by the smaller body before collision is (in $R$)

State whether the following statements are true or false:
$(a)$ The intensity of the Earth's gravitational field increases as we move higher above the Earth's surface.
$(b)$ There is no atmosphere on the Moon because the escape velocity on the Moon is small.
$(c)$ $A$ satellite orbiting the Earth is in a state of weightlessness.

Two satellites $s_1$ and $s_2$ of equal masses revolve in the same sense around a heavy planet in coplanar circular orbits of radii $R$ and $4R$. Which of the following statements is correct?

If the height of a satellite from the surface of the Earth is increased,then its

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 $({T_{is}})$