Kepler's third law states that square of period of revoluation (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T² = Kr³ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = $${{GMm} \over {{r^2}}}$$, here G is gravitational constant. The relation between G and K is described as

Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 $$ \times $$ 10²⁴ kg) have to be compressed to be a black hole?

A particle of mass 'm' is kept at rest at a height 3R from the surface of earth, where 'R' is radius of earth and 'M' is mass of earth. The minimum speed with which it should be projected , so that it does not return back, is
(g is acceleration due to gravity on the surface of earth)