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MHT CET20239 May 2023Morning ShiftMathematicsApplication of DerivativesActual

An object is moving in the clockwise direction around the unit circle x^2+y^2=1 . As it passes through the point ( 1 2 , 3 2 ) , its y -co-ordinate is decreasing at the rate of 3 units per sec. The rate at which the x -co-ordinate changes at this point is

Options

  1. A2 units / sec
  2. B3 3 units / sec
  3. C3 units / sec
  4. D2 3 units / sec

Correct answer

B. 3 3 units / sec

Step-by-step solution

Given equation is x^2+y^2=1 Differentiating w.r.t. t, we get aligned & 2 x d x dt +2 y d y dt =0 & 2 x d x dt +2 y(-3)=0 & d x dt = 6 y 2 x & d x dt = 3 y x & . d x dt |_ ( 1 2 , 3 2 ) = 3 3 2 1 2 & =3 3 units/sec aligned

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