Newton's Law of Cooling question from MHT CET 2024 (10 May, Shift 2)

Answer: (d)

1. Newton's law: $\frac{T_1 - T_2}{t} = k\left(\frac{T_1 + T_2}{2} - \theta\right)$.
2. First $t$: $\frac{\theta}{t} = k(3.5\theta - \theta) = 2.5k\theta$
3. Next $t$: $\frac{3\theta - T}{t} = k\frac{\theta + T}{2}$
4. Dividing: $15\theta - 5T = \theta + T \Rightarrow T = \frac{7\theta}{3}$
5. So the answer is (d) $\frac{7\theta}{3}$.