Which of the following statements about the universal gravitational constant, G, is true?

Analyze the question: We need to find the true statement about the universal gravitational constant, G.

Concept: Newton's law of gravitation says F = GMm/r², so

G = Fr²/(Mm)

Step-by-step solution:

1. Dimension of force: F = MLT⁻²
2. Dimension of r²: L²
3. Dimension of Mm: M²

G = (MLT⁻² × L²) / M² = M⁻¹L³T⁻²

Checking each option:

• A. Fundamental quantity: False. Fundamental (base) quantities are mass, length, time, and so on. G is a derived constant, and its dimension is built from M, L and T.
• B. Dimension M⁻¹L³T⁻²: True, as shown above.
• C. S.I. unit N m² kg: False. The correct unit is N m² kg⁻², not N m² kg. The kg should be in the denominator and squared.
• D. Vector quantity: False. G is a scalar constant with magnitude only (6.67 × 10⁻¹¹ N m² kg⁻²).

Tip: For dimension questions, rearrange the formula to make the required constant the subject, then substitute the dimensions of each term. Also remember that the unit of G is N m² kg⁻², which is the same as m³ kg⁻¹ s⁻².