What would be the value of g on the surface of the earth if its mass was twice and its radius half of what it is now?

The acceleration due to gravity is given by the formula, g = G M R 2 where g is the acceleration due to gravity, G is the universal gravitational constant, M is the mass of the planet and R is the radius of the planet. If the mass of the earth becomes twice and radius becomes half then the value of g becomes g ' = G M ' R ' 2 = G ( 2 M ) R 2 2 = 2 G M R 2 4 = 2 × 4 G M R 2 = 8 G M R 2 = 8 g . Thus, the new value of g is eight times its original value.

A metal ball of mass 5 kg falls from a height of 490 m . How much time it will take to reach the ground? ( g = 9 . 8 m / s 2 )

Given data s = 490 m a = g = 9 . 8 m / s 2 u = 0 m / s s = u t + 1 2 a t 2 490 = 0 × t + 1 2 × 9 . 8 × t 2 t 2 = 100 t = 10 s This is the required time.