Weight of the body on the surface of the earth is 64 N . What will be the gravitational force acting on it, if it is taken up to a height equal to ( 1 3 )^ r d of the radius of the earth from the earth's surface?

Step-by-step solution

The weight of a body on the surface of the earth is given by W = mg = GMm R^2 = 64 N, where M is the mass of the earth and R is the radius of the earth. When the body is taken to a height h = R 3 above the surface of the earth, the distance from the center of the earth becomes r = R + h = R + R 3 = 4R 3 . The gravitational force F at this height is given by F = GMm r^2 = GMm ( 4R 3 )^2 = GMm 16R^2 9 = 9 16 GMm R^2 . Substituting the value of the weight on the surface W = GMm R^2 = 64 N into the equation for F , we