NEET 2020 Physics Question 174 Solution

The heat required to raise the temperature of a body by $$\Delta T$$ is given by: $$Q = m s \Delta T$$, where $$m$$ is mass and $$s$$ is specific heat capacity.

For a solid sphere of uniform density $$\rho$$ and radius $$r$$: $$V = \frac{4}{3}\pi r^3$$ $$m = \rho V = \rho \left(\frac{4}{3}\pi r^3\right)$$ Because both spheres are made of copper, density $$\rho$$ and specific heat $$s$$ are identical.

$$Q = \left[\rho \left(\frac{4}{3}\pi r^3\right)\right] s \Delta T$$ For identical $$\Delta T = 1\text{ K}$$: $$Q \propto r^3$$.

$$\frac{Q_1}{Q_2} = \left(\frac{r_1}{r_2}\right)^3 = (1.5)^3 = \left(\frac{3}{2}\right)^3 = \frac{27}{8}$$. Matches Option 1.