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AP EAMCET202017 Sep 2020Morning ShiftPhysicsMotion in Two DimensionsActual

If mass, speed and radius of the circular path of the particle are increased by (100 % ), then the necessary force required to maintain the circular path will have to be increased by

Options

  1. A(100 % )
  2. B(250 % )
  3. C(300 % )
  4. D(400 % )

Correct answer

C. (300 % )

Step-by-step solution

Centripetal force is given as (F= m v^2 r ) where, (m= ) mass, (v= ) velocity and (r= ) radius. ( F₂ F₁ = m₂ m₁ ( v₂ v₁ )^2 ( r₁ r₂ ) ) ...(i) When, mass, speed and radius of circular path of particle increases by (100 % ), i.e. these become double. Hence, ( aligned & m₂=2 m₁ & v₂=2 v₁ & r₂=2 r₁ aligned ) ( ) From Eq. (i), we have ( aligned & F₂ F₁ & = 2 m₁ m₁ ( 2 v₁ v₁ )^2 ( r₁ 2 r₁ )=2 4 1 2 =4 & F₂ & =4 F₁ aligned ) Percentage increase in centripetal force, (= F₂-F₁ F₁ 100= 4 F₁-F₁ F₁ 100=300 % )

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