The universal constant of gravitation G has the unit

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NDA-I (GAT) Official Paper (Held On: 13 Apr, 2025)
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  1. N
  2. m/s
  3. Joule
  4. N·m²/kg²

Answer (Detailed Solution Below)

Option 4 : N·m²/kg²
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Detailed Solution

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Calculation:

From Newton's law:

F = G × (m1 × m2) / r2

Rearranging for G:

G = F × r2 / (m1 × m2)

⇒ F (N) = kg × m/s2, r2 = m2, m1, m2 = kg

⇒ G = (kg × m/s2) × m2 / (kg × kg)

⇒ G = N · m2 / kg2

∴ The SI unit of G is N · m2 / kg2.

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