The magnitude of gravitational potential energy of a body at a distance ' R ' from the centre of the earth is ' E '. Its weight at a distance ' 1.5 R ' from the centre of the earth is

Step-by-step solution

Given a gravitational potential energy E = GMm R , where M is Earth's mass, m is the body's mass, and G is the gravitational constant, we find that GMm = ER . The weight at distance 1.5R equals the gravitational force there: W' = GMm (1.5R)^2 . Substituting GMm = ER yields W' = ER (1.5R)^2 = ER 2.25R^2 = E 2.25R . Since 2.25 = 9 4 , this simplifies to W' = 4E 9R , corresponding to option C.