F=mw^2r analysis demension
Answers
Explanation:
we have to derive F = mv²/r using dimensional analysis where F is centripetal force, m is mass, v is velocity and r is radius of the circular path of the body.
dimensional formula of F = [MLT-²]
dimensional formula of m = [M]
dimensional formula of v = [LT-¹]
dimensional formula of r = [L]
now, let F ∝ m^xv^yr^z
⇒[MLT-²] ∝ [M]^x [LT-¹]^y [L]^z
⇒[MLT-²] ∝ [M^x L^(y + z) T^-y]
on comparing both sides,
x = 1, y + z = 1 , y = 2
so, z = -1
now, F ∝ m¹v²r-¹
⇒F ∝ mv²/r
⇒F = mv²/r , let proportionality constant is 1.
hence, it is clear that F = mv²/r from dimensional analysis.
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