A metallic sphere cools from

(2) From Newton's Law of cooling,

$\frac{T_{1}-T_{2}}{t}=K\left[\frac{T_{1}+T_{2}}{2}-T_{0}\right]$

Here, $\mathrm{T}_{1}=50^{\circ} \mathrm{C}, \mathrm{T}_{2}=40^{\circ} \mathrm{C}$

and \mathrm{T}_{\mathrm{o}}=20^{\circ} \mathrm{C}, \mathrm{t}=600 \mathrm{~S}=5$ minutes

$\Rightarrow \frac{50-40}{5 \mathrm{Min}}=K\left(\frac{50+40}{2}-20\right)$             .....(i)

Let $T$ be the temperature of sphere after next 5 minutes. Then

$\frac{40-T}{5}=K\left(\frac{40+T}{2}-20\right)$                    ....(ii)

Dividing eqn. (ii) by (i), we get

$\frac{40-T}{10}=\frac{40+T-40}{50+40-40}=\frac{T}{50}$

$\Rightarrow 40-T=\frac{T}{5} \Rightarrow 200-5 T=T$

$\therefore T=\frac{200}{6}=33.3^{\circ} \mathrm{C}$