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Dimensional Analysis

Question

The physical quantities which do not have same dimensions are
Energy and Torque
Strain and Youngs Modulus
Pressure and Stress
Work and Energy

A

Strain and Youngs Modulus

B

Energy and Torque

C

Pressure and Stress

D

Work and Energy

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Solution

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The energy and torque have the same dimensions as both can be represented as the product of force and distance.

The pressure and stress are the quantities that have the same dimensions. They both are defined as force per unit area.

The work and energy are the quantities that have the same dimensions. They are the product of force and distance.

The young's modulus is defined as the ratio of stress and strain. The strain is a dimensionless quantity. So, Young's modulus will have the same unit as of stress.
Strain = $\frac{c h a n g e i n d i m e n s i o n}{o r g i n a l d i m e n s i o n}$
$= M^{0} L^{0} T^{0}$

Youngs Modulus $= M L^{- 1} T^{- 2}$

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