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Question

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?
  1. Gch3/2
  2. hGc3/2
  3. hGc5/2
  4. hcG

A
Gch3/2
B
hGc3/2
C
hGc5/2
D
hcG
Solution
Verified by Toppr

The correct option is B hGc3/2
The SI unit of h is J.s or N.m.s and SI unit of c is m/s and Si unit of G is N.m2/kg2

For A: (N.m2/kg2)(m/s)(N.m.s)3/2=kg.m3N.s5=kg.m3(kg.m/s2)(s5)=m2/s3

For B: (N.m.s)(N.m2/kg2)(m/s)3/2=Ns2kg=(kg.m/s2)(s2)kg=m, it is the unit length.

For C: (N.m.s)(N.m2/kg2)(m/s)5/2=Ns3m.kg=(kg.m/s2)(s3)m.kg=s

For D: (N.m.s)(m/s)N.m2/kg2=kg

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