Q121 / 160 · TS EAMCET 2007 · Physics
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
- A(iv) (iii) (ii) (i)
- B(ii) $\begin{array}{ll}\text { (i) } & \text { (iii) }\end{array}{(iv)}$
- C(iii) $\quad$ (ii) $\quad$ (i) $\quad$ (iv)
- Correct answerD(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.
Hence, the correct answer is option: 'D'.