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?
√Gch3/2
√hGc3/2
√hGc5/2
√hcG
A
√Gch3/2
B
√hGc3/2
C
√hGc5/2
D
√hcG
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Solution
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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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