Student Login

Home›Chapters›Units, Dimensions and Measurement PYQs›Applications of Dimensional Analysis›Question 67

NEET 2016 (Phase 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from NEET 2016 (Phase 2)

Q67NEET 2016 · PHASE 2Medium

Applications of Dimensional Analysis

Planck's constant (h), speed of light in vacuum (c) and Newton's gravitional constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?

Show answer and solution

Answer: (a)

$[hG] = ML^2T^{-1}\cdot M^{-1}L^3T^{-2} = L^5T^{-3}$ , so $[\sqrt{hG}] = L^{5/2}T^{-3/2}$ .
$[c^{3/2}] = L^{3/2}T^{-3/2}$ .
$\dfrac{\sqrt{hG}}{c^{3/2}}$ has dimension $L$ .
So the answer is (a).

Report a mistake

More questions on Applications of Dimensional Analysis

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the…NEET 2015 (AIPMT, Cancelled Paper)
If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant…JEE Main 2015 (11 Apr, Shift 1)
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)