The Question is from NEET guide , and it was created by the author Mr. ANIL KUMAR.G

Question

The dimensional formula of gravitational potential is:

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [Option C]
## CONCEPT FRAMEWORK
**Primary Concept**: Dimensional Analysis
**Related Topics**: Gravitational Potential Energy, Work-Energy Theorem, Dimensions of Physical Quantities
**Prerequisites**: Definition of Gravitational Potential, Dimensional analysis of work and mass.
## SOLUTION PATHWAY
**Given Information**:
 Gravitational Potential is defined as the work done per unit mass to bring a small mass from infinity to that point.
**Method & Steps**:
1. Identify the definition of gravitational potential:
   Reasoning: Gravitational potential (V) is the gravitational potential energy (U) per unit mass (m), i.e., V = U/m
   Formula/Rule:  $V = \frac{U}{m}$
2. Determine the dimensional formula of gravitational potential energy:
   Reasoning: Gravitational Potential Energy is equivalent to work done. Work done is force times distance.
   Working:  Work = Force * Distance =  mass * acceleration * distance , Dimensionally is $[M][LT^{-2}][L] = [ML^2T^{-2}]$
    Key Point: The dimensions for force are $[MLT^{-2}]$ , and for distance is $[L]$
3. Calculate the dimensional formula of gravitational potential
   Reasoning: Divide the dimensional formula of gravitational potential energy by mass.
   Working:  $[V] = \frac{[ML^2T^{-2}]}{[M]} = [L^2T^{-2}]$
    Result: The dimensional formula of gravitational potential is $[L^2T^{-2}]$
   Verification: The calculated dimension matches with option C.
 ## OPTION ANALYSIS
[A] :x: [This is the dimensional formula for energy or work, not potential.]
[B] :x: [This is not a standard formula of any potential.]
[C] ✓: [This is the correct dimensional formula for gravitational potential.]
[D] :x: [This is the dimensional formula for acceleration, not potential.]
 ## LEARNING AIDS
**Common Mistakes**:
1.  [Error 1]: Confusing Gravitational Potential with Gravitational Potential Energy. [How to avoid]: Remember that potential is potential energy per unit mass, so you need to divide by mass.
2. [Error 2]: Incorrectly determining the dimensions of work or energy. [How to avoid]: Remember that work is force times distance and force is mass times acceleration.
**Quick Tips**:
1. [Helpful shortcut]: Remember the dimensional formula for energy and divide by mass when calculating potential.
2. [Memory aid]: Think of potential as energy per unit mass to easily derive the dimensional formula.

Mr. ANIL KUMAR.G · Answer

$[ML^2T^{-2}]$

Mr. ANIL KUMAR.G · Answer

$[ML^2T^{-3}]$

Mr. ANIL KUMAR.G · Answer

The correct Option is "$[L^2T^{-2}]$"

Mr. ANIL KUMAR.G · Answer

$[LT^{-2}]$

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