Q96 / 180 · NEET 2020 (Phase 1) · Physics

The quantities of heat required to raise the temperature of two solid copper spheres of radii $r_{1}$ and $r_{2} (r_{1} = 1.5 r_{2})$ through $1 K$ are in the ratio:

Solution

Heat supplied $Δ Q = M s Δ T$

For same material ' $s$ ' same.

$Δ Q \propto M$ and $M = \frac{4}{3} π r^{3} ρ$

$Δ Q \propto r^{3}$

$\frac{Δ Q_{1}}{Δ Q_{2}} = {(\frac{r_{1}}{r_{2}})}^{3} = {(\frac{1.5}{1})}^{3} = \frac{27}{8}$

Hence, the correct answer is option: 'D'.