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MHT CET20243 May 2024Evening ShiftMathematicsApplication of DerivativesActual

If a body cools from 80^ C to 60^ C in the room temperature of 30^ C in 30 min , then the temperature of a body after one hour is

Options

  1. A42^ C
  2. B24^ C
  3. C48^ C
  4. D56^ C

Correct answer

C. 48^ C

Step-by-step solution

Let be the temperature of the body at any time ' t '. array ll & d dt ( -30) & d dt =k( -30) array Integrating on both sides, we get array ll & ( -30)=k t+C & when t =0, =80^ C & (80-30)= k (0)+ C & C= 50 array array ll & ( -30)= kt + 50 ...(i) & When t =30, =60 & 30=30 k + 50 & 30- 50=30 k & k = 1 30 ( 3 5 ) array Equation (i) becomes, ( -30)= 1 30 ( 3 5 ) t+ 50 when t=60 minutes, we have aligned & ( -30)= 1 30 ( 3 5 ) 60+ 50 & ( -30)=2 ( 3 5 )+ 50 & ( -30)= ( 9 25 50 ) & -30=18 & =48^ C aligned

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