Q80 / 90 · JEE Main 2021 (27 Jul Shift 1) · Physics

A body takes $4 \min$ to cool from $61 ° C$ to $59 ° C .$ If the temperature of the surroundings is $30 ° C,$ the time taken by the body to cool from $51 ° C$ to $49 ° C$ is:

Solution

$\frac{Δ T}{Δ t} = K (T_{t} - T_{S}) T_{t} =$ average temperature

$T_{S} =$ surrounding temperature

$\frac{61 - 59}{4} = K (\frac{61 + 59}{2} - 30)$ $. . . (i)$

$\frac{51 - 49}{t} = K (\frac{51 + 49}{2} - 30) . . . (ii)$

Divide $(1)$ and $(2)$

$\frac{t}{4} = \frac{60 - 30}{50 - 30} = \frac{30}{20}$

So, $t = 6$ $\min$

Hence, the correct answer is option: 'D'.