Which one of the following pairs does not have the same dimension?

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Q: 81 (NDA-I/2010)

Which one of the following pairs does not have the same dimension?

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,8,15,8,8,5,2

keywords: 

{'same dimension': [0, 0, 1, 0], 'potential energy': [0, 0, 1, 4], 'kinetic energy': [0, 0, 4, 7], 'specific gravity': [0, 0, 3, 1], 'gravitational force': [0, 0, 0, 6], 'frictional force': [0, 0, 1, 0], 'height': [0, 0, 1, 2], 'density': [2, 0, 1, 3], 'focal length': [1, 0, 5, 7]}

The correct answer is option 2: Density and specific gravity.

The dimension of a physical quantity refers to the type of units used to measure that quantity. When two physical quantities have the same dimension, it means that they can be measured using the same units.

Option 1: Potential energy and kinetic energy both have the same dimension, which is energy. Both can be measured in joules (J) or any other unit of energy.

Option 2: Density and specific gravity do not have the same dimension. Density is the mass per unit volume and is typically measured in kilograms per cubic meter (kg/m^3) or grams per cubic centimeter (g/cm^3). On the other hand, specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). It is a dimensionless quantity and does not have any units. Therefore, they do not have the same dimension.

Option 3: Focal length and height also do not have the same dimension. Focal length is a measure of the distance between the center of a lens or mirror and its focal point and is typically measured in meters (m) or centimeters (cm). Height, on the other hand, is a measure of distance and