The Question is from neet-physics units-and-measurement conversion-of-units-for-one-system-to-another, and it was created by the author VENKATESWARARAO

Question

The dimensions of universal gravitational constant are

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Dimensional Analysis of Physical Quantities
	**Related Topics**: Gravitational Force, Units and Dimensions
	**Prerequisites**: Understanding of the Law of Universal Gravitation and the concept of dimensional analysis.
## SOLUTION PATHWAY
**Given Information**:
	The Law of Universal Gravitation: $F = G \frac{m_1 m_2}{r^2}$, where F is force, G is the gravitational constant, $m_1$ and $m_2$ are masses, and r is the distance.
**Method & Steps**:
	1.  Isolate G: Rearrange the formula to solve for G: $G = \frac{F r^2}{m_1 m_2}$
		Reasoning: To find the dimensions of G, we need an equation where G is isolated.
		Formula/Rule: $F = G \frac{m_1 m_2}{r^2}$ rearranged to $G = \frac{F r^2}{m_1 m_2}$
	2.  Substitute the dimensions of each quantity:  Force (F) has dimensions of $MLT^{-2}$, distance (r) has dimensions of L, and mass (m) has dimensions of M.
		Working: $G = \frac{[MLT^{-2}] [L^2]}{[M][M]} = \frac{ML^3T^{-2}}{M^2}$
		Key Point: Dimensions are treated as algebraic variables.
	3. Simplify the expression: $G = M^{-1}L^3T^{-2}$
		Result:  The dimensions of G are $M^{-1}L^3T^{-2}$
		Verification:  The derived dimensions match option B.
 ## OPTION ANALYSIS
[A] :x: Incorrect dimensions.
[B] ✓: Correct dimensions of the universal gravitational constant.
[C] :x: Incorrect dimensions.
[D] :x: Incorrect dimensions.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. [Error 1]: Incorrectly identifying the dimensions of force. [How to avoid]: Memorize or derive the dimensions of force ($MLT^{-2}$) using Newton's second law.
		2. [Error 2]: Making algebraic errors in simplifying the dimensions. [How to avoid]: Double-check the cancellation and exponents.
	**Quick Tips**:
		1. [Helpful shortcut]: Remember the formula of gravitational force and isolate G.
		2. [Memory aid]: Memorize the dimensions of force, mass, and distance.

VENKATESWARARAO · Answer

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

VENKATESWARARAO · Answer

The correct Option is "${M^{ - 1}}{L^3}{T^{ - 2}}$"

VENKATESWARARAO · Answer

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

VENKATESWARARAO · Answer

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

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