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

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?

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

The radius of a planet is twice the radius of earth. Both have almost equal average mass densities. V_P and V_E are escape velocities of the planet and the earth, respectively, then