Match List-I with List-II. List-I: (A) Gravitational constant, (B) Gravitational potential energy, (C) Gravitational potential, (D) Acceleration due to gravity. List-II: (I) [LT⁻²], (II) [L²T⁻²], (III) [ML²T⁻²], (IV) [M⁻¹L³T⁻²]. Choose the correct match.
Options

Question

Match List-I with List-II. List-I: (A) Gravitational constant, (B) Gravitational potential energy, (C) Gravitational potential, (D) Acceleration due to gravity. List-II: (I) [LT⁻²], (II) [L²T⁻²], (III) [ML²T⁻²], (IV) [M⁻¹L³T⁻²]. Choose the correct match.

Options

G1 Physics · Accepted Answer

Gravitational constant: F = Gm₁m₂/r² ⇒ [G] = [F][r²]/[m₁m₂] = (MLT⁻²)(L²)/M² = M⁻¹L³T⁻². So A–IV. Gravitational potential energy has the dimension of energy: [U] = ML²T⁻². So B–III. Gravitational potential is potential energy per unit mass: [V] = [U]/M = L²T⁻². So C–II. Acceleration due to gravity has dimension [g] = LT⁻². So D–I. Hence the correct matching is A–IV, B–III, C–II, D–I. Correct option: C.