Some physical constants are given in List-I and their dimensional formulae are given in List-II. Match the…

Some physical constants are given in List-I and their dimensional formulae are given in List-II. Match the following $\begin{array}{l}
\text{List-I} & \text{List-II} \\
\text{(A) Planck's constant} & (e) \left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right] \\
\text{(B) Gravitational constant} & (f) \left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right] \\
\text{(C) Bulk modulus} & (g) \left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right] \\
\text{(D) Coefficient of viscosity} & (h) \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] \\
\end{array}$ The correct answer is
  1. A-h, B-g, C-e, D-f
  2. A-f, B-e, C-g, D-h
  3. A-g, B-h, C-e, D-f
  4. A-g, B-f, C-e, D-h

Solution

(1) Planck's constant $\begin{aligned} {[h] } & =\left[\frac{E}{v}\right] \\ & =\frac{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}{\left[\mathrm{T}^{-1}\right]}=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]\end{aligned}$ (2) Gravitational constant $\begin{aligned} {[G] } & =\left[\frac{F r^2}{m_1 m_2}\right] \\ & =\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{\left[\mathrm{M}^2\right]} \\ & =\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\end{aligned}$ (3) Bulk modulus $\begin{aligned} {[B] } & =\frac{[\text { Normal stress }]}{[\text { Volumetric strain }]} \\ & =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\end{aligned}$ (4) Coefficient of viscosity, $\begin{aligned} \eta & =\frac{[F]}{[A][d v / d y]}=\frac{\left[\mathrm{ML}^{-2}\right][\mathrm{L}]}{\left[\mathrm{L}^2\right]\left[\mathrm{LT}^{-1}\right]} \\ & =\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]\end{aligned}$ Hence, option (d) is correct. *

Asked in: JEE Mains - Units and Dimensions - Test 2

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