Question

derive the dimensional formula for hc/G

Answer 1

h is plank's constant
c is speed of light
G is gravitational constant.

we know, energy of photon = hc/wavelength
dimension of hc = dimension of energy × length

dimension of energy = [ML²T-²]
dimension of wavelength = [L]
so, dimension of hc = [ML²T-²] [L] = [ML³T-²]

now, dimension of G :
we know, gravitational force , F = GMm/r²
so, dimension of G = {F × r²/Mm}

dimension of force = [MLT-²]
dimension of r² = [L²]
dimension of M = [M]
dimension of m = [M]
so, dimension of G = [MLT-²][L²]/[M][M]
= [M-¹L³T-²]

now, dimension of hc/G = dimension of hc/dimension of G
= [ML³T-²]/[M-¹L³T-²]
= [M²]