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NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

Some physical constants are given in List-I and their dimensional...

Some physical constants are given in List-I and their dimensional formulae are given in List-II. Match the following (
List-IList-II
(1)Planck's constant(i)\left[ML^{-1} T^{-2}\right]
(2)Gravitational constant(ii)\left[ML^{-1} T^{-1}\right]
(3)Bulk modulus(iii)\left[ML^2 T^{-1}\right]
(4)Coefficientof viscosity</td><td>(iv)</td><td>\left[\mathrm{M}^{-1}L^3 T^{-2}\right]
) The correct answer is

Options

  1. A(iv) (iii) (ii) (i)
  2. B(ii) $\begin{array}{ll}\text{ (i) } & \text{ (iii) }\end{array}{(iv)}$
  3. C(iii) \quad (ii) \quad (i) \quad (iv)
  4. D(iii) (iv) (i) (ii)

Correct answer

D. (iii) (iv) (i) (ii)

Step-by-step solution

(1) Planck's constant [h]=[Ev]=[ML2T−2][T−1]=[ML2T−1]\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 [G]=[Fr2m1m2]=[MLT−2][L2][M2]=[M−1L3T−2]\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 [B]=[ Normal stress ][ Volumetric strain ]=[ML−1T−2]\begin{aligned} {[B] } & =\frac{[\text{ Normal stress }]}{[\text{ Volumetric strain }]} \\ & =\left[\mathrm{ML}^{-1} \mathrm{ T}^{-2}\right]\end{aligned} (4) Coefficient of viscosity, η=[F][A][dv/dy]=[ML−2][L][L2][LT−1]=[ML−1T−1]\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.
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