NDA (I) 2022 General Ability Test · Question 68 of 150

Correct — B, M⁻¹L³T⁻². From Newton's law F = G·m₁m₂/r², rearranged G = F·r²/(m₁m₂). Substituting the dimensions gives [MLT⁻²][L²]/[M²] = M⁻¹L³T⁻².

• (a)ML³T⁻² — This keeps mass to the +1 power. But the two masses in the denominator contribute M⁻², while force gives M⁺¹, so the net mass power is M⁻¹, not M⁺¹.
• (c)M²L⁻²T⁻² — Both powers are wrong: the length power should be +3 (from r²), not −2, and the net mass power is −1, not +2.
• (d)M²L⁻¹T⁻² — This inverts the length dependence and gets the mass power wrong; the correct result is M⁻¹L³T⁻².

The universal gravitational constant G appears in Newton's law F = G·m₁m₂/r². Solving for G gives G = F·r²/(m₁m₂). Its dimensional formula, M⁻¹L³T⁻², follows by substituting the dimensions of force (MLT⁻²), distance squared (L²) and the product of two masses (M²).

Work from the defining equation rather than memory. Force is MLT⁻², r² is L², and dividing by m₁m₂ (M²) subtracts 2 from the mass power: 1 − 2 = −1. That single step separates the right answer from the traps.

• Newton's law of gravitation: F = G·m₁m₂/r².
• The dimensional formula of G is M⁻¹L³T⁻².
• The SI unit of G is N·m²·kg⁻², with value about 6·674 × 10⁻¹¹.
• G is a universal constant — the same everywhere — unlike g (acceleration due to gravity), which varies with place.

• Getting the mass power wrong by forgetting the two masses in the denominator.
• Confusing G with g.

A dimensional-formula recall, or a derive-from-the-equation item using F = G·m₁m₂/r².

No directly related past PYQ was found.

• practice — not a real PYQ

  The dimensional formula of the acceleration due to gravity g is

  • (a)LT⁻²
  • (b)MLT⁻²
  • (c)L²T⁻²
  • (d)MLT⁻¹

  Answer(a) LT⁻² — g is an acceleration, so length per time squared.

• practice — not a real PYQ

  The SI unit of the universal gravitational constant G is

  • (a)N m kg⁻¹
  • (b)N m² kg⁻²
  • (c)N kg⁻²
  • (d)N m² kg⁻¹

  Answer(b) N m² kg⁻² — from G = F·r²/(m₁m₂).