A body of mass $m$ falls from a height $R$ above the surface of the earth, where $R$ is the radius of the earth. What is the velocity attained by the body on reaching the ground? (Acceleration due to gravity on the surface of the earth is $g$)

A satellite $S$ moves around a planet $P$ in an elliptical orbit as shown in figure. The ratio of the speed of the satellite at point $a$ to that at point $b$ is 

The variation of acceleration due to gravity $ ( g )$ with distance $(r)$ from the center of the earth is correctly represented by ... (Given $R =$ radius of earth)

The height at which the weight of a body becomes $1/16^{th}$, its weight on the surface of earth (radius $R$), is

If the acceleration due to gravity at earth is $'g'$ and mass of earth is $80$ times that of moon and radius of earth is $4$ times that of moon, the value of acceleration due to gravity at the surface of moon will be

Figure shows the orbit of a planet $P$ round the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse.

If $t_1$ is the time taken by the planet to travel along $ACB$ and $t_2$ the time along $BDA,$ then