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MHT CET20242 May 2024Morning ShiftMathematicsApplication of DerivativesActual

A spherical metal ball at 80^ C cools in 5 minutes to 60^ C , in surrounding temperature of 20^ C , then the temperature of the ball after 20 minutes is approximately

Options

  1. A(8.15)^ C
  2. B(11.85)^ C
  3. C(28.15)^ C
  4. D(31.85)^ C

Correct answer

D. (31.85)^ C

Step-by-step solution

Let be the temperature of ball at any time ' t '. aligned & d dt ( -20) & d dt =- k ( -20), k 0 aligned Integrating on both sides, we get | -20|=- kt + c when t =0, =80^ array ll & c= 60 & | -20|=-k t+ 60...(i) array aligned & When t =5, =60^ & 40=-5 k + 60 & 5 k = 60- 40 & 5 k = ( 3 2 ) & k = 1 5 ( 3 2 ) aligned | -20|= -1 5 ( 3 2 ) t + 60 ...[From (i)] when t =20 , aligned & | -20|= -1 5 ( 3 2 ) 20+ 60 & | -20|=-4 ( 3 2 )+ 60 & | -20|= ( 2 3 )^4+ 60 & | -20|= ( 16 60 81 ) & | -20|= (11.85) & -20=11.85 & =11.85+20

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