MHT CET202618 April 2026Morning ShiftMathematicsDifferential EquationsActual
A body cools from 100^ C to 60^ C in 20 minutes, the temperature of the surroundings being 20^ C . The total time taken (in minutes) for the body to cool down to 40^ C is ...
Options
- A60
- B40
- C50
- D30
Correct answer
B. 40
Step-by-step solution
Using Newton's law of cooling: ( T₁ - T_s T₂ - T_s ) = kt For the first interval, the body cools from 100^ C to 60^ C in 20 minutes with T_s = 20^ C : ( 100 - 20 60 - 20 ) = k(20) ( 80 40 ) = 20k (2) = 20k For the total time t to cool from 100^ C to 40^ C : ( 100 - 20 40 - 20 ) = kt ( 80 20 ) = kt (4) = kt 2 (2) = kt Substituting 20k for (2) : 2(20k) = kt t = 40 minutes Answer: 40