Dimensional Analysis

Easyphysics

If gravitational potential energy between two masses is U = - G m_1 m_2 / r, what are dimensions of G?

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$M^{- 1} L^{3} T^{- 2}$

$M L^{- 3} T^{2}$

$M^{- 2} L^{3} T^{- 2}$

$M L T^{- 2}$

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About This Question

Subject: physics
Chapter: physics and measurement
Topic: dimensional analysis
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

$M^{- 1} L^{3} T^{- 2}$

Rearranging the formula to solve for the Universal Gravitational Constant $G$ : $G = \frac{U \cdot r}{m _{1} \cdot m _{2}}$ Now, substitute the dimensions of each quantity:

$[U]$ (Energy) = $[M L^{2} T^{- 2}]$
$[r]$ (Distance) = $[L]$
$[m_{1}, m_{2}]$ (Mass) = $[M]$ $[G] = \frac{[ M L ^{2} T ^{- 2} ] \cdot [ L ]}{[ M ] \cdot [ M ]} = \frac{[ M L ^{3} T ^{- 2} ]}{[ M ^{2} ]} = [M^{- 1} L^{3} T^{- 2}]$ .

This easy difficulty physics question is from the chapter physics and measurement, covering the topic of dimensional analysis. It appeared in the 2025 exam.

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