A satellite A of mass m is at a distance r from the surface of the earth. Another satellite B of mass 2 m is at a distance of 2 r from the earth's surface. Their time periods are in the ratio of

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B?

The largest and the shortest distance of the earth from the sun are r₁ and r₂. Its distance from the sun when it is perpendicular to the major axis of the orbit drawn from the sun is

The escape velocity of a sphere of mass m is given by (G = universal gravitational constant, M_e = mass of earth and Re = radius of earth)

A body of mass m is placed on earth's surface. It is then taken from earth's surface to a height h = 3R, then the change in gravitational potential energy is

If the gravitational force between two objects were proportional to ¹/R (and not as ¹/R²), where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

What will be the formula of the mass in terms of g, R and G? (R = radius of earth)

The distance of two planets from the sun are 10¹³ and 10¹² m respectively. The ratio of time periods of these two planets is

The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?