Question

The unit of universal gravitational constant is :

• A. \( Nm^2 \, kg^2 \)
• B. \( Nm^{-2} \, kg^{-2} \)
• C. \( Nm^{-2} \, kg^2 \)
• D. \( Nm^2 \, kg^{-2} \)

Hint:

Always derive units from formula instead of memorizing—this avoids confusion in exponents.

Answer 1

The Correct Option is D

Step 1: Use Newton’s law of gravitation.
\[ F = G \frac{m_1 m_2}{r^2} \]

Step 2: Rearrange to find unit of \( G \).
\[ G = \frac{F r^2}{m_1 m_2} \]

Step 3: Substitute SI units.
Force \( F \) has unit Newton \( (N) \), distance \( r \) has unit meter \( (m) \), and mass has unit kilogram \( (kg) \).
\[ G = \frac{N \cdot m^2}{kg \cdot kg} \]
\[ = Nm^2 kg^{-2} \]

Step 4: Conclusion.
\[ \boxed{Nm^2 kg^{-2}} \]