Question

if velocity of light, acceleration due to gravity and atmospheric pressure are basic quantities find dimension of length

Answer 1

The velocity of light = c

acceleration due to gravity = g

Pressure = p

Now we know that acceleration due to gravity = length/time²

=> g = L/T²

also,

speed = length/time

=> c = L/T

squaring on both the sides we get,

c² = L²/T²

=> c² = (L/T²) x L

substituting g = L/T² , we get

c² = gL

=> L = c²/g

Hence the dimension of Length is [ c² g⁻¹]