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MHT CET202211 Aug 2022Morning ShiftMathematicsDifferential EquationsActual

If a body is heated to 110^ C and placed in air at 10^ C after 1 hour its temperature is 60^ C , then the additional time required for it to cool to 30^ C is

Options

  1. A5 2 hrs
  2. B2 5 hrs
  3. C( 5 2 -1 ) hrs
  4. D( 5 2 +1 ) hrs

Correct answer

C. ( 5 2 -1 ) hrs

Step-by-step solution

aligned & d T ~d t =-K(T-10) & T-10=e^ -k t+C & T=10+e^C e^ -k t aligned For t=0 , aligned & T=110 & e^C=100 i.e. & T=10+100 e^ -k t aligned For t=1 , aligned & T=60 & 60=10+100 e^ -k 1 & -k= 1 2 & k= 2 aligned T=10+100 e^ - ( ₂ ) t Putting T=30 aligned & 30=10+100 e^ - ( ₂ ) t & ( 1 5 )=-( 2) t & t= 5 2 aligned Additional time =t-1= 5 log2 -1

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