Question

Obtain an expression for the centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r . Take dimensionless constant K = 1 .

Answer 1

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here is your ans

Answer 2

The centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r is  F = K m v² / r

Stepwise calculations

         F ∝ mᵃ vᵇ rˣ           (where m is mass, v is velocity and r is the radius)

         F = K mᵃ vᵇ rˣ                       (Given K = 1)

   

We know that,    F = [ M¹ L¹ T⁻²]

                  F = K mᵃ vᵇ rˣ  and   F = [ M¹ L¹ T⁻²]

                    F = [M]ᵃ [LT⁻¹]ᵇ [L]ˣ           ( v = [LT⁻¹] )

                          [M¹]ᵃ [L¹T⁻¹]ᵇ [L¹]ˣ

                           [Mᵃ] [LᵇT⁻ᵇ] [Lˣ]  

                    F =  [Mᵃ Lᵇ⁺ˣ T⁻ᵇ]

      Compairing, F = [ M¹ L¹ T⁻²]  and   F =  [Mᵃ Lᵇ⁺ˣ T⁻ᵇ]

   We get,

• a = 1.
• -b = -2   → b = 2
• b+x =1   →  2+x =1  → x = -1

Substituting the values of a, b and x  in F = K mᵃ vᵇ rˣ

              F = K m¹ v² r⁻¹

               F = K m v² / r

An expression for the centripetal force F acting on a particle of mass m moving with velocity v in a circle of radius r is F = K m v² / r

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