Ncert Exercises & Solutions

31. Give an example of

(a) a physical quantity which has a unit but no dimensions
(b) a physical quantity which has neither unit nor dimensions
(c) a constant which has a unit
(d) a constant which has no unit

Hint: A quantity that is a ratio of similar quantities can be dimensionless or unitless.

Step 1: Find the quantities that are dimensionless or unitless.

\begin{array}{l} (a) Plane angle θ = \frac{L}{r} radian \\ its unit is radian but has no dimensions \\ (b) Strain = \frac{ΔL}{L} = \frac{Change in length}{length} \\ It has neither unit nor dimensions \\ (c) Gravitational constant (G) = 6 .67 \times 10^{- 11} N - m^{2} / {kg}^{2} \\ (d) Reynold's number is a constant which has no unit. \end{array}

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