Student Login

Home›Chapters›Units, Dimensions and Measurement PYQs›Applications of Dimensional Analysis›Question 55

JEE Main 2020 (9 Jan, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2020 (9 Jan, Shift 1)

Q55JEE Main 2020 · 9 JAN · SHIFT 1Easy

Applications of Dimensional Analysis

A quantity f is given by $f = \sqrt{\frac{hc^5}{G}}$ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of:

Show answer and solution

Answer: (a)

$[hc^5] = ML^2T^{-1}\cdot L^5T^{-5} = ML^7T^{-6}$ .
Dividing by $[G] = M^{-1}L^3T^{-2}$ : $M^2L^4T^{-4}$ .
Square root: $ML^2T^{-2}$ , the dimension of energy.
So the answer is (a) energy.

Report a mistake

More questions on Applications of Dimensional Analysis

The force ' F ' acting on a body of density ' d ' are related by the relation F = y/√(d)…MHT CET 2019 (2 May, Shift 2)
In the formula X = 5YZ2, X and Z have dimensions of capacitance and magnetic field…JEE Main 2019 (10 Apr, Shift 2)
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the…JEE Main 2019 (11 Jan, Shift 2)
Expression for time in terms of G (universal gravitational constant), h (Planck constant)…JEE Main 2019 (9 Jan, Shift 2)
The force of interaction between two atoms is given by F = αβ exp (-(x²)/(α kT)); where x…JEE Main 2019 (11 Jan, Shift 1)
If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken…JEE Main 2019 (8 Apr, Shift 2)
The density of a material in SI units is 128 kg m–3. In certain units in which the unit…JEE Main 2019 (10 Jan, Shift 1)
The characteristic distance at which quantum gravitational effects are significant, the…JEE Main 2018 (15 Apr, Shift 2)