Question

A spherical body having radius $r$ is radiating energy $Q$ at a given temperature. If its radius is doubled then for same time, energy radiated will be

• A. $\frac{1}{2}Q$
• B. $\frac{1}{4}Q$
• C. $2Q$
• D. $4Q$

Answer 1

The correct option is D $4Q$

We know, emissive power, $E=\frac{Q}{At}$
where $Q$ is energy emitted, $A$ is the surface area of body and $t$ is time.
$\Rightarrow Q=EAt$
$\Rightarrow Q\propto A$ $[$ material and time are same $]$
$\Rightarrow Q\propto r^2$ $[A=4\pi r^2]$
If radius is doubled then energy emitted will be $4$ times the initial value.