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 List-I (1) Planck's constant (2) Gravitational constant (3) Bulk modulus (4) Coefficient of viscosity List-II (i) $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$ (ii) $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$ (iii) $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$ (iv) $\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$ The correct answer is
  1. (iv) (iii) (ii) (i)
  2. (ii) $\begin{array}{ll}\text { (i) } & \text { (iii) }\end{array}{(iv)}$
  3. (iii) $\quad$ (ii) $\quad$ (i) $\quad$ (iv)
  4. (iii) (iv) (i) (ii)

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: AP EAMCET 2007

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