1.

The Centripetal Force (f) Acting On A Particle (moving Uniformly In A Circle) Depends On The Mass (m) Of The Particle, Its Velocity (v) And Radius (r) Of The Circle. Derive Dimensionally Formula For Force (f)?

Answer»

GIVEN, F ∝ ma.vb.rc

∴ F = kma.vb.rc (where K is CONSTANT)

Putting dimensions of each quantity in the equation,

 [M1L1T-2] = [M1L0T0]a.[M0L1T-1]b. [M0L1T0]C = [MaLb+cT+cT-b]

⇒ a =1, b +c = 1, -b = -2

⇒ a= 1, b = 2, c = -1

∴ F = km1.v2.r-1= kmv2/r

Given, F ∝ ma.vb.rc

∴ F = kma.vb.rc (where k is constant)

Putting dimensions of each quantity in the equation,

 [M1L1T-2] = [M1L0T0]a.[M0L1T-1]b. [M0L1T0]c = [MaLb+cT+cT-b]

⇒ a =1, b +c = 1, -b = -2

⇒ a= 1, b = 2, c = -1

∴ F = km1.v2.r-1= kmv2/r



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