A metallic sphere cools from 50 degree C to
Question:

A metallic sphere cools from $50^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ in $300 \mathrm{~s}$. If atmospheric temperature around is $20^{\circ} \mathrm{C}$, then the sphere’s temperature after the next 5 minutes will be close to:

1. $33^{\circ} \mathrm{C}$

2. $35^{\circ} \mathrm{C}$

3. $31^{\circ} \mathrm{C}$

4. $28^{\circ} \mathrm{C}$

Correct Option: 1

Solution:

$\frac{50-40}{300}=\beta\left(\frac{50+40}{2}-20\right)$

$\frac{40-\mathrm{T}}{300}=\beta\left(\frac{40+\mathrm{T}}{2}-20\right)$

$\therefore \mathrm{T}=\frac{100}{3}$