The Question is from neet-physics properties-solids-liquids stress-and-strain, and it was created by the author SUBHANI

Question

What are the dimensions of stress?

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option A
## CONCEPT FRAMEWORK
 **Primary Concept**: Stress and its derivation from force and area.
 **Related Topics**: Pressure, Strain, Young's Modulus, Elasticity.
 **Prerequisites**: Understanding of dimensional analysis and basic physics units (mass, length, time).
## SOLUTION PATHWAY
**Given Information**:
  The question asks for the dimensions of stress.
  [Important conditions]: None explicitly stated, but we need to recall the definition of stress.
**Method & Steps**:
 1. Define stress:
  Reasoning: Stress is defined as force per unit area ($\sigma = \frac{F}{A}$).
  Formula/Rule: $\sigma = \frac{F}{A}$ 
 2. Determine the dimensions of force and area:
  Working: Force ($F$) has dimensions of $[MLT^{-2}]$ (Newton's second law: $F = ma$). Area ($A$) has dimensions of $[L^2]$.
  Key Point:  It's crucial to know the base units of force and area.
 3. Calculate the dimensions of stress:
  Result: The dimensions of stress are $[MLT^{-2}]/[L^2] = [ML^{-1}T^{-2}]$.
  Verification: We can verify this by checking the units: Pascals (Pa) are $N/m^2$, which are equivalent to $kg \cdot m \cdot s^{-2} / m^2 = kg \cdot m^{-1} \cdot s^{-2}$.
 ## OPTION ANALYSIS
[A] ✓: $[ML^{-1}T^{-2}]$ is the correct dimensional formula for stress, as derived above.
[B] :x: $[MLT^{-2}]$ represents the dimensions of force, not stress.
[C] :x: $[ML^2T^{-2}]$ represents the dimensions of energy or work, not stress.
[D] :x: $[M^0L^0T^0]$ represents dimensionless quantities.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing stress with force or pressure: Remember stress is force per unit *area*, not just force.
  2. Incorrectly applying dimensional analysis rules: Ensure you correctly handle the division of dimensions.
 **Quick Tips**:
  1. Remember the basic dimensions of force and area to quickly derive the dimensions of stress.
  2. Use the unit Pascal (Pa) as a memory aid; its dimensions are equivalent to the dimensions of stress.

SUBHANI · Answer

The correct Option is "$[ML^{-1}T^{-2}]$"

SUBHANI · Answer

$[MLT^{-2}]$

SUBHANI · Answer

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

SUBHANI · Answer

$[M^0L^0T^0]$

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