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JEE Main 20199 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2019 · 9 January · Evening Shift · Physics · Units and Dimensions

Expression for time in terms of G (universal gravitational...

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

Options

  1. AGhc3\sqrt{\dfrac{Gh}{{c}^{3}}}
  2. Bhc5G\sqrt{\dfrac{h{c}^{5}}{G}}
  3. CGhc5\sqrt{\dfrac{Gh}{{c}^{5}}}
  4. Dc3Gh\sqrt{\dfrac{{c}^{3}}{Gh}}

Correct answer

C. Ghc5\sqrt{\dfrac{Gh}{{c}^{5}}}

Step-by-step solution

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

\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}
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