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Dimensional formula of universal gravitational constant $G$ is-

The gravitational force between two bodies is $6.67×10_{−7}N$ when the distance between their centres is 10 m. If the mass of first body is 800 kg, then the mass of second body is :

Two metal spheres of the same material and radius $r$ are in contact with each other. The gravitational force of attraction between the spheres is given by:

The radius and density of two artificial satellites are $R_{1}$ , $R_{2}$ and $ρ_{1}$, $ρ_{2}$ respectively. The ratio of accelerations due to gravity on them will be:

The average density of the earth in terms of $g,G$and $R$ is:

If the Earth were compressed in such a way that its mass remained the same, but the distance around the equator were just one-half what it is now, what would be the acceleration due to gravity at the surface of the Earth?

If $R$ is radius of the earth and $W$ is work done in lifting a body from the ground to an altitude $R$, the work which should be done in lifting it further to twice that altitude is:

The Jupiter's period of revolution around the Sun is $12$ times that of the Earth. Assuming the planetary orbits to be circular, find the acceleration of Jupiter in the heliocentric reference frame.

In the solar system, the Sun is in the focus of the system for Sun-Earth binding system. Then the binding energy for the system will be $($given that radius of the Earth's orbit around the Sun is $1.5×10_{11}$ m and mass of Earth is $6×10_{24}kg$ $)$

$Massofthesunis10_{30}kg$

The orbital speed for an Earth satellite near the surface of the Earth is 7 km/sec. If the radius of the orbit is 4 times the radius of the Earth, the orbital speed would be