Verified Solution • 2025–26 Session moderate

QNEET-2016-Ph-1179: NEET 2016 Physics - Class 11 NEET-2016-Ph-1179 Solution: Planck's constant (h) speed of light in vacuum (c) and Newton's …

Planck's constant (h) speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length? hGc3/2\sqrt{\frac{hG}{c^{3/2}}} hGc5/2\sqrt{\frac{hG}{c^{5/2}}} hcG\sqrt{\frac{hc}{G}} Gch3/2\sqrt{\frac{Gc}{h^{3/2}}}

Multiple Choice Options

  • A hGc3/2{{\sqrt {hG} } \over {{c^{3/2}}}} c 3/2 h G _ _
  • B hGc5/2{{\sqrt {hG} } \over {{c^{5/2}}}} c 5/2 h G _ _
  • C hcG\sqrt {{{hc} \over G}} G h c _ _
  • D Gch3/2\sqrt {{{Gc} \over {{h^{3/2}}}}} h 3/2 G c _ _

Step-by-Step Verified Solution

According to question, L _ h p c q G r [M 0 LT 0 ] = [ML 2 T -1 ] p [LT -1 ] q [M -1 L 3 T -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 = 1 2 , q = _ 3 2 _ L = h G c 3 / 2

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