The dimension of universal gravitational constant is……….?

Analyze the question: We need the dimensional formula of the universal gravitational constant, G.

Concept: Newton's law of gravitation says

F = G m₁m₂ / r²

Rearranging for G:

G = F r² / (m₁ m₂)

Solution:

Dimensions of each quantity:

• Force, F = MLT⁻²
• Distance squared, r² = L²
• Mass product, m₁m₂ = M²

Substitute:

G = (MLT⁻² × L²) / M²

G = ML³T⁻² / M²

G = M⁻¹L³T⁻²

Checking the options:

• A. M⁻¹L³T⁻², which matches our result.
• B. ML³T², which has the wrong powers of M and T.
• C. ML³, which is incomplete.
• D. MLT⁻², which is the dimension of force, not G.

The SI unit of G is N·m²/kg², which is m³ kg⁻¹ s⁻². This agrees with M⁻¹L³T⁻².

Exam tip: For dimension questions, start from a formula that contains the quantity, make it the subject, and replace each term with its dimensions. Remember that force is MLT⁻². You can also check by converting the units: m³ kg⁻¹ s⁻² gives L³ M⁻¹ T⁻² straight away.