Two satellites of masses $m$ and $1.5 m$ are revolving around the earth in two circular orbits of heights $R_E$ and $2 R_E$ respectively,where $R_E$ is the radius of the earth. The ratio of the minimum and maximum gravitational forces exerted by the two satellites on the earth is

The solar constant on the surface of the earth is $S$. What will be its value on the surface of another planet which is about $5.3 \, AU$ away from the sun?

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 $({T_{is}})$

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
$Assertion$ $(A)$: The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
$Reason$ $(R)$: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements,choose the most appropriate answer from the options given below:

If a tunnel is cut at any orientation through the Earth,a ball released from one end will reach the other end in time ........ $\text{min}$ (neglect Earth's rotation).

The ratio of the $K.E.$ required to be given to a satellite to escape Earth's gravitational field to the $K.E.$ required to be given so that the satellite moves in a circular orbit just above Earth's atmosphere is: