Question

Two perfectly conducting spheres of the same metal have radii $3$cm and $6$cm respectively and are $10$${}^o$C and $15$${}^o$C hotter than the surroundings.The ratio of loss of heat of the spheres is

• A. 1 : 6
• B. 4 : 3
• C. 4 : 9
• D. 1 : 16

Answer 1

The correct option is A 1 : 6

We know that: $Q\propto AT$
$\frac{Q_1}{Q_2}=\frac{r_1^2{T}_1}{r_2^2{T}_2}$
$\frac{Q_1}{Q_2}=\frac{3^2}{6^2}\times \frac{10}{15}=\frac{1}{6}$