Question

A solid sphere of copper of radius R and hollow sphere of the same material of inner radius r and outer radius R are heated to the same temperature and allowed to cool in the same environment. Which of them starts cooling faster?

• A. copper sphere
  
• B. Hollow sphere.
• C. cant say
  
• D. both

Answer 1

Answer: (B)

Hollow sphere.

$\text{Solution}:$

Since the temperature and surface area is same, therefore the energy emitted per second by both spheres is same. We know that

$Q=mc\Delta T$

Since Q is same and c is also same (both copper).

$\therefore M\propto \frac{1}{\Delta T}$

Mass of hollow sphere is less, therefore Temperature change will be more.

$\therefore$ Hollow sphere will cool faster.

$\text{Hence B is the correct option}$