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MHT CET20192 May 2019Morning ShiftMathematicsApplication of DerivativesActual

A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermostripple increases at the rate of 5 c m / s e c . Then area increased after 2 seconds is ________

Options

  1. A100 π c m 2 / s e c
  2. B40 c m 2 / s e c
  3. C50 c m 2 / s e c
  4. D25 c m 2 / s e c

Correct answer

A. 100 π c m 2 / s e c

Step-by-step solution

Given: d r d t = 5 c m / s e c ⇒ d r = 5 d t t h e n r = 5 t + c , at t = 0 , ⇒ r = 0 ⇒ c = 0 r = 5 t New A = π r 2 ⇒ d A d t = 2 π r d r d t = 2 π . 10.5 at t = 2 ⇒ r = 10 = 100 π c m 2 / s e c .

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