Question

Derive F=mv^2/r using dimensional analysis where f is centiputal force. M is mass and v is velocity r is radius of circular path of the body

Answer 1

Hope u got my approach, i use shortcuts, i solved this question roughly .

Answer 2

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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