Question

What is the relationship between these expressions:
d^2 ∝ L^3 = d ∝ L^(3/2) = (d/L) ∝ L^(1/2)
Can I get its simplification

Answer 1

they all are the same
we have d^2 proportional to L^3
d^2 ∝ L^3
take square root on both sides
d ∝ L^(3/2)
L^3/2= L* L^(1/2)
so
d∝ L* L^(1/2)
divide both sides by L
d/L ∝ L^(1/2)
so we see these all are same, but their form is changed

Answer 2

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