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Units and Measurement question

2016 · Q161
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Units and Measurement question

2016 · Q161

NEETPhysicsUnits and MeasurementMCQ+4 / −1
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 ?
  1. A
    hGc3/2{{\sqrt {hG} } \over {{c^{3/2}}}}c3/2hG​​
  2. B
    hGc5/2{{\sqrt {hG} } \over {{c^{5/2}}}}c5/2hG​​
  3. C
    hcG\sqrt {{{hc} \over G}}Ghc​​
  4. D
    Gch3/2\sqrt {{{Gc} \over {{h^{3/2}}}}}h3/2Gc​​
View written solutionFree

Correct answer: A

According to question,

L ∝\propto∝ hp cq Gr

[M0LT0] = [ML2T-1]p [LT-1]q [M-1L3T-2]r

Equating power both sides, we get

p - r = 0        ......(1)

2p + q + 3r = 1        ......(2)

- p - q - 2r = 0        ......(3)

Solving equation (1), (2), (3), we get

p = r = 12{1 \over 2}21​, q = −32 - {3 \over 2}−23​

∴\therefore∴ L = hGc3/2{{\sqrt {hG} } \over {{c^{3/2}}}}c3/2hG​​

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