Question

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_1$ and $r_2(r_1=1.5r_2)$ through $1\text{K}$ are in the ratio

• A. $9:4$
• B. $3:2$
• C. $5:3$
• D. $27:8$

Answer 1

The correct option is D $27:8$

We know that heat required,

$Q=ms\Delta T=(\frac{4}{3}\pi r^3\times \rho )s\Delta T$

[$\because$ mass = density$\times$ volume]

For same material and for same temperature change

$Q\propto r^3........\left(1\right)$

So, $\frac{Q_1}{Q_2}={\left(\frac{r_1}{r_2}\right)}^3$

Substituting the given data we get,

$\frac{Q_1}{Q_2}={\left(\frac{1.5r_2}{r_2}\right)}^3=\frac{27}{8}\Rightarrow Q_1:Q_2=27:8$

Hence, option (d) is the correct answer.

Why this question? Concept involved: 1. Specific heat. 2.Density. This question is asked in NEET 2020 and similar model questions are asked in JEE mains.