The energy E of a body moving in a circular path is assumed to depend only on mass m, speed v and radius r. Dimensional analysis alone can determine E ∝:
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The energy E of a body moving in a circular path is assumed to depend only on mass m, speed v and radius r. Dimensional analysis alone can determine E ∝:

G1 Physics · Accepted Answer

Let E ∝ mᵃvᵇrᶜ. Comparing [ML²T⁻²] gives a=1, -b=-2 ⇒ b=2, and b+c=2 ⇒ c=0. Thus E ∝ mv². Dimensional analysis cannot determine the dimensionless numerical factor.