NEETPhysicsGravitation
A body of mass ' m ' is raised from the surface of the Earth to various heights ' h '. Match List-I (Height h ) with List-II (Work done against gravity) and select the correct option. (where ' R ' is the radius of the Earth and ' g ' is the acceleration due to gravity on the surface of the Earth) List-I List-II (A) h = R (I) mgR (B) h = 2R (II) mg R 2 (C) h = 3R (III) 2 3 mgR (D) h (IV) 3 4 mgR
Options
- A(A) - (II), (B) - (III), (C) - (IV), (D) - (I)
- B(A) - (I), (B) - (II), (C) - (III), (D) - (IV)
- C(A) - (IV), (B) - (III), (C) - (II), (D) - (I)
- D(A) - (II), (B) - (IV), (C) - (III), (D) - (I)
Correct answer
A. (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
Step-by-step solution
The work done in raising a mass m from the surface of the Earth to a height h is equal to the change in its gravitational potential energy. Initial potential energy at the surface, U_i = - GMm R . Final potential energy at height h , U_f = - GMm R+h . Work done, W = U_f - U_i = GMm R - GMm R+h = GMmh R(R+h) . Using GM = gR^2 , we get W = mgh 1 + h R . For (A) h = R : W = mgR 1 + 1 = mg R 2 . (Matches II) For (B) h = 2R : W = mg(2R) 1 + 2 = 2 3 mgR . (Matches III) For (C) h = 3R : W = mg(3R) 1 + 3 = 3 4 mgR . (Match