Question

One of the combinations from the fundamental physical constants is hc/G. The unit of this expression is
a) kg²
b) m³
c) s⁻¹
d) m

Answer 1

we know, E = hν
here , ν is the frequency and E is the energy if photon
so, unit of h = J.s = kgm²/s

unit of speed of light = unit of speed = m/s
so, unit of c = m/s

we know, Gravitational law,
F = GMm/r² ⇒G = Fr²/Mm
so, unit of G = unit of F.unit of r²/unit of mass²
Unit of G = m³/Kg.s²

Now, unit of hc/G = [kgm²/s][m/s]/[m³/kg.s²] = kg²
Hence, option (a) is correct

Answer 2

Answer:

we know, E = hν

here , ν is the frequency and E is the energy if photon

so, unit of h = J.s = kgm²/s

unit of speed of light = unit of speed = m/s

so, unit of c = m/s

we know, Gravitational law,

F = GMm/r² ⇒G = Fr²/Mm

so, unit of G = unit of F.unit of r²/unit of mass²

Unit of G = m³/Kg.s²

Now, unit of hc/G = [kgm²/s][m/s]/[m³/kg.s²] = kg²

Hence, option (a) is correct