Q164 / 180 · COMEDK 2025 (10 May Shift 3) · Physics
The unit of universal gravitational constant is :
- A$\mathrm{N} \mathrm{m}^{-2} \mathrm{~kg}^{-2}$
- B$\mathrm{N} \mathrm{m}^{-2} \mathrm{~kg}^2$
- C$\mathrm{N} \mathrm{m}^2 \mathrm{~kg}^2$
- Correct answerD$\mathrm{N} \mathrm{m}^2 \mathrm{~kg}^{-2}$
Solution
The law of universal gravitation is given by the formula $F = G \dfrac{m_1 m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the universal gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them.
Rearranging the formula to solve for $G$, we get $G = \dfrac{F r^2}{m_1 m_2}$.
Substituting the SI units for each quantity: $F$ is in Newtons ($\mathrm{N}$), $r$ is in meters ($\mathrm{m}$), and $m$ is in kilograms ($\mathrm{kg}$).
The unit of $G$ is $\dfrac{\mathrm{N} \cdot \mathrm{m}^2}{\mathrm{kg} \cdot \mathrm{kg}} = \mathrm{N} \cdot \mathrm{m}^2 \cdot \mathrm{kg}^{-2}$.
Answer: $\mathrm{N} \mathrm{m}^2 \mathrm{~kg}^{-2}$
Rearranging the formula to solve for $G$, we get $G = \dfrac{F r^2}{m_1 m_2}$.
Substituting the SI units for each quantity: $F$ is in Newtons ($\mathrm{N}$), $r$ is in meters ($\mathrm{m}$), and $m$ is in kilograms ($\mathrm{kg}$).
The unit of $G$ is $\dfrac{\mathrm{N} \cdot \mathrm{m}^2}{\mathrm{kg} \cdot \mathrm{kg}} = \mathrm{N} \cdot \mathrm{m}^2 \cdot \mathrm{kg}^{-2}$.
Answer: $\mathrm{N} \mathrm{m}^2 \mathrm{~kg}^{-2}$
Hence, the correct answer is option: 'D'.