NDA (I) 2025 General Ability Test · Question 131 of 150

Correct — D, N-m^2/kg^2. Newton's law of gravitation, F = GMm/r^2, gives G = F.r^2/(M.m). Substituting the units: (N x m^2)/(kg x kg) = N-m^2/kg^2 (equivalently m^3 kg^-1 s^-2).

• (a)N — The newton is the unit of force (F), not of the gravitational constant G.
• (b)m/s — Metre per second is the unit of speed or velocity, unrelated to G.
• (c)Joule — The joule is the unit of energy or work, not of G.

The universal gravitational constant G is the proportionality constant in F = GMm/r^2. Rearranging gives G = F.r^2/(M.m), so its units follow from those of force, distance and mass: N-m^2/kg^2. Numerically G is about 6.674 x 10^-11 N-m^2/kg^2.

Derive the unit from the formula rather than memorising blindly. Force contributes newtons, r^2 contributes m^2, and the two masses contribute kg^2, landing on N-m^2/kg^2. The other options are units of force, speed and energy — quick eliminations.

• Newton's law of gravitation: F = GMm/r^2.
• G = F.r^2/(M.m), so its SI unit is N-m^2/kg^2 (= m^3 kg^-1 s^-2).
• Numerically G is about 6.674 x 10^-11 N-m^2/kg^2.
• G is a universal constant; g (acceleration due to gravity, about 9.8 m/s^2) is different and varies with location.

• G (the universal constant, N-m^2/kg^2) is not g (about 9.8 m/s^2).
• Derive the unit from F = GMm/r^2; the newton alone is force, not G.

Asks for the unit or dimensional formula of a physical constant (G, h, and so on), or to distinguish G from g.

No directly related past PYQ was found.

• practice — not a real PYQ

  The approximate value of the universal gravitational constant G is

  • (a)9.8 N-m^2/kg^2
  • (b)6.67 x 10^-11 N-m^2/kg^2
  • (c)6.67 x 10^11 N-m^2/kg^2
  • (d)3 x 10^8 N-m^2/kg^2

  Answer(b) 6.67 x 10^-11 N-m^2/kg^2.

• practice — not a real PYQ

  The SI unit of the acceleration due to gravity g is

  • (a)N-m^2/kg^2
  • (b)m/s^2
  • (c)joule
  • (d)newton

  Answer(b) m/s^2 — g is an acceleration, unlike the constant G.