The mass of the sun is 2 × 10 30 kg and the mass of the earth is 6 × 10 24 kg . If the average distance between the sun and the earth be 1 . 5 × 10 8 km , calculate the force of gravitation between them.(Take: G = 6 . 7 × 10 - 11 N m 2 kg - 2 )

Given, Mass of the sun, m 1 = 2 × 10 30 kg Mass of earth, m 2 = 6 × 10 24 kg Average distance between the sun and earth, d = 1 . 5 × 10 8 km , Gravitational constant, G = 6 . 7 × 10 - 11 N m 2 kg - 2 From Newton's universal law of gravitation, gravitational force, F = G × m 1 × m 2 d 2 → 1 Substituting the given values in equation 1 , we get F = 6 . 7 × 10 - 11 × 2 × 10 30 × 6 × 10 24 1 . 5 × 10 8 × 10 3 × 1 . 5 × 10 8 × 10 3 ⇒ 6 . 7 × 2 × 6 × 10 21 1 . 5 × 1 . 5 ⇒ 3 . 573 × 10 22 N

A piece of stone is thrown vertically upwards. It reaches maximum height in 3 seconds. If the acceleration of stone be 9 . 8 m s 2 directed towards ground, calculate the initial velocity of stone with which it is thrown upwards.

Given t = 3 s From, equations of motion we get v = u + g t where v = final velocity u = initial velocity g = acceleration due to gravity t = time taken by body to reach from initial velocity u to final velocity v . Final velocity of the stone will become zero, when it reaches maximum height. So, v = 0 Since the stone is travelling against the gravity(upwards), g = - 9 . 8 m s - 2 So, substituting above values, we get, 0 = u - ( 9 . 8 × 3 ) ⇒ u = 27 . 4 m s .