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MHT CET202122 Sep 2021Evening ShiftMathematicsApplication of DerivativesActual

A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is 3 ~mm . and 1 hour later has been reduced to 2 ~mm , then the expression of radius r of the raindrop at any time t is (where 0 t < 3 )

Options

  1. Ar = t +5
  2. Br=t-5
  3. Cr =3- t
  4. Dr=t+3

Correct answer

C. r =3- t

Step-by-step solution

We have dv dt - (4 r ^2 ) We know that v = 4 3 r ^2 dv dt =4 r ^2 dr dt aligned & 4 r ^2 dr dt - (4 r ^2 ) & 4 r ^2 dr dt = (-4 k r ^2 ) dr dt =- k aligned

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