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

Question

Which of the following sets have different dimensions?

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [D]
## CONCEPT FRAMEWORK
	**Primary Concept**: Dimensional Analysis
	**Related Topics**: Units and Measurements, Physical Quantities
	**Prerequisites**: Understanding of fundamental physical quantities and their units.
## SOLUTION PATHWAY
**Given Information**:
	Sets of physical quantities.
	The correct answer is the set with different dimensions.
**Method & Steps**:
	1.  Determine the dimensions of each physical quantity in each set.
		Reasoning: Compare the dimensions within each set to see if they are consistent. Dimensions are fundamental properties like mass [M], length [L], and time [T], and sometimes electric current [A].
		Formula/Rule: Pressure and Stress are Force/Area (MLT^-2/L^2 = ML^-1T^-2), Young's Modulus is also Stress/Strain, strain is dimensionless, therefore same dimensions as pressure and stress.
	2. Analyze each option.
		Working:
		  A. Pressure: [ML⁻¹T⁻²], Young's modulus: [ML⁻¹T⁻²], Stress: [ML⁻¹T⁻²] - All have same dimensions.
		  B. Emf: [ML²T⁻³A⁻¹], Potential difference: [ML²T⁻³A⁻¹], Electric potential: [ML²T⁻³A⁻¹] - All have same dimensions.
		  C. Heat: [ML²T⁻²], Work done: [ML²T⁻²], Energy: [ML²T⁻²] - All have same dimensions.
		  D. Dipole moment: [LTA], Electric flux: [ML³T⁻³A⁻¹], Electric field: [MLT⁻³A⁻¹] - These have different dimensions.
	3.  Identify the set with different dimensions.
		Result: Option D has quantities with different dimensions.
		Verification: The dimensions of each quantity have been derived correctly.
 ## OPTION ANALYSIS
[A] :x: Pressure, Young's modulus, and stress all have the same dimensions, [ML⁻¹T⁻²].
[B] :x: Emf, potential difference, and electric potential all have the same dimensions, [ML²T⁻³A⁻¹].
[C] :x: Heat, work done, and energy all have the same dimensions, [ML²T⁻²].
[D] ✓: Dipole moment, electric flux, and electric field have different dimensions. Dipole moment is [LTA], electric flux is [ML³T⁻³A⁻¹], and electric field is [MLT⁻³A⁻¹].
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing units with dimensions. Dimensions are fundamental, while units are how we measure them.
		2.[Error 2]:  Incorrectly remembering the dimensions of common physical quantities.
	**Quick Tips**:
		1. Start by writing down the definition of each quantity in terms of basic quantities like force, length, mass and time.
		2.Use the definitions to derive the dimensions. Force is [MLT-2].

ABDUL JILANI BASHA · Answer

Pressure, Young’s modulus, Stress

ABDUL JILANI BASHA · Answer

Emf, Potential difference, Electric potential

ABDUL JILANI BASHA · Answer

Heat, Work done, Energy

ABDUL JILANI BASHA · Answer

The correct Option is "Dipole moment, Electric flux, Electric  field "

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