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Q80 (NDA-I/2010) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

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

Result
Your answer: —  Â·  Correct: B
Explanation

In dimensional analysis, physical quantities are expressed in terms of fundamental dimensions like Mass [M], Length [L], and Time [T] [t1][t2]. Potential and kinetic energy both represent energy with the dimensional formula [ML2T-2] [t4]. Focal length and height are both measurements of length [L] [t2]. Gravitational and frictional forces are both types of force with dimensions [MLT-2] [t5]. However, density and specific gravity differ significantly. Density is mass per unit volume, having dimensions [ML-3] [t2][c3]. In contrast, specific gravity is the ratio of the density of a substance to the density of a reference (usually water), making it a dimensionless quantity [c3]. Since one has dimensions and the other is dimensionless, they do not share the same dimension, making option 2 the correct answer.

Sources

  1. [1] https://personalpages.manchester.ac.uk/staff/david.d.apsley/lectures/hydraulics2/t3.pdf
  2. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 2: The Solar System > 2.3. The Sun > p. 23
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