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Q16 (CISF/2019) Science & Technology › Basic Science (Physics, Chemistry, Biology)

Which one of the following pairs of quantities has no length in their dimension?

Explanation

The dimension of a physical quantity describes the powers of fundamental units (Mass, Length, Time) it contains. A quantity has "no length" if the exponent of Length (L) in its dimensional formula is zero (L0).

  • Surface Tension: Defined as Force per unit Length (F/l). Its dimensions are [MLT-2] / [L] = [M1L0T-2].
  • Strain: Defined as the ratio of change in length to original length (ΔL/L). It is dimensionless, represented as [M0L0T0].

Both quantities in Option B have L0. In other options, Angular Momentum has [ML2T-1], Mass Density has [ML-3], and Pressure Gradient has [ML-2T-2], all of which involve length. While Angle is dimensionless ([L0]), its pair in option D (Pressure Gradient) contains length.

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