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MHT CET20244 May 2024Morning ShiftMathematicsApplication of DerivativesActual

A wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet hung in the open air loses half its moisture during the first hour, then the time t , in which 99 % of the moisture will be lost, is

Options

  1. A2 10 2
  2. B10 2
  3. C3 10 2
  4. D1 2 10 2

Correct answer

A. 2 10 2

Step-by-step solution

Let y be the amount of moisture at time t . aligned & d y dt =- y & ~d y y =- dt aligned Integrating on both sides, we get d y y =- dt y=- t + c when t =0, y=1 From (i), we get c =0 ...(i) when t =1, y=0.5 From (i) and (ii), we get array ll & (0.5)=- & = 2 array From (i), (ii) and (iii), we get y=-( 2) t When 99 % of the moisture will be lost, array ll & y=0.01 & (0.01)=-( 2) t & t= 2 10 2 array

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