Units & Dimensions

JEE Main level, single correct, medium

74 of 149

Question 74 of 149

If the velocity of light cc, universal gravitational constant GG and planck's constant hh are chosen as fundamental quantities. The dimensions of mass in the new system is:

Show answer and solution

Answer: (D) [h12c12G−12]\left[{h}^{\dfrac{1}{2}}{c}^{\dfrac{1}{2}}{G}^{-\dfrac{1}{2}}\right]

If EE is energy, then
[E]=[Gm1m2r]\left[E\right]=\left[\dfrac{G{m}_{1}{m}_{2}}{r}\right]
[E][r]=[Gm1m2]\left[E\right]\left[r\right]=\left[G{m}_{1}{m}_{2}\right]
Since E=hcλE=\dfrac{hc}{\lambda }
[hcλ][r]=[Gm1m2]⇒[hc][L][L]=[G][M2]\left[\dfrac{hc}{\lambda }\right]\left[r\right]=\left[G{m}_{1}{m}_{2}\right] \Rightarrow \dfrac{\left[hc\right]}{\left[L\right]}\left[L\right]=\left[G\right]\left[{M}^{2}\right]
(both λ\lambda and rr have dimensions of length)
∴[hcG]=[M]∴\left[\sqrt{\dfrac{hc}{G}}\right]=\left[M\right]

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.

More Physics practice

JEE Main Physics practice question on Units & Dimensions (Dimensions), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.