Units & Dimensions

JEE Main level, single correct, medium

126 of 149

Question 126 of 149

Expression for time in terms of GG (universal gravitational constant), hh (Planck constant) and cc (speed of light) is proportional to:

Show answer and solution

Answer: (C) Ghc5\sqrt{\dfrac{Gh}{{c}^{5}}}

t=Gα.hβcrt={G}^{\alpha .}{h}^{\beta }{c}^{r}

[T]=(M−1L3T−2)α(ML2T−1)β[LT−1]γ\left[T\right]={\left({M}^{-1}{L}^{3}{T}^{-2}\right)}^{\alpha }{\left(M{L}^{2}{T}^{-1}\right)}^{\beta }{\left[L{T}^{-1}\right]}^{\gamma }

=M−α+βL3α+2β+γT−2α−β−γ={M}^{-\alpha +\beta }{L}^{3\alpha +2\beta +\gamma }{T}^{-2\alpha -\beta -\gamma }

−α+β=0-\alpha +\beta =0

3α+2β+γ=03\alpha +2\beta +\gamma =0

−2α−β−γ=1-2\alpha -\beta -\gamma =1

∴α=12;β=12;γ=−52∴\alpha =\dfrac{1}{2};\beta =\dfrac{1}{2};\gamma =\dfrac{-5}{2}

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.