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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)? |
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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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