Student Login

Home›Chapters›Units, Dimensions and Measurement PYQs›Applications of Dimensional Analysis›Question 69

JEE Main 2015 (11 Apr, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2015 (11 Apr, Shift 1)

Q69JEE Main 2015 · 11 APR · SHIFT 1Medium

Applications of Dimensional Analysis

If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum $\mu$ 0 can be expressed in units of:

Show answer and solution

Answer: (c)

The fine-structure constant $\dfrac{e^2}{4\pi\varepsilon_0\hbar c}$ is dimensionless.
With $\varepsilon_0 = \dfrac{1}{\mu_0c^2}$ it becomes $\dfrac{\mu_0 c e^2}{2h}$ , still dimensionless.
So $[\mu_0] = \left[\dfrac{h}{ce^2}\right]$ .
So the answer is (c).

Report a mistake

More questions on Applications of Dimensional Analysis

If the capacitance of a nanocapacitor is measured in terms of a unit 'u' made by…JEE Main 2015 (10 Apr, Shift 1)
If dimensions of critical velocity v c of a liquid flowing through a tube are expressed…NEET 2015 (AIPMT)
A beaker contains a fluid of density ρ kg / m3, specific heat S J/kgoC and viscosity η…JEE Main 2015 (11 Apr, Shift 1)
If force (F), velocity (V) and time (T) are taken as fundamental units, then dimensions…NEET 2014 (AIPMT)
From the following, the quantity (constructed from the basic constants of nature), that…JEE Main 2013 (9 Apr, Shift 1)
A metal sample carrying a current along X-axis with density Jx is subjected to a magnetic…JEE Main 2013 (25 Apr, Shift 1)
If the time period t of the oscillation of a drop of liquid of density d, radius r…JEE Main 2013 (23 Apr, Shift 1)
The density of a material in CGS system of units is 4 g cm ⁻³. In a system of units in…NEET 2011 (AIPMT, Mains)