Question

The sun radiates energy at the rate of $3.6\times {10}^{26}{\text{Js}}^{-1}$. The rate of decrease in mass of sun is $\left({\text{in kgs}}^{-1}\right)$

• A. $3.6\times {10}^{36}$
• B. $12\times {10}^{10}$
• C. $1.3\times {10}^{20}$
• D. $4\times {10}^9$

Answer 1

The correct option is D $4\times {10}^9$

According to mass energy equivalence,
$E=m{c}^2$

$\Rightarrow \frac{dE}{dt}=\left(\frac{dm}{dt}\right)c^2$

Given that,
$\frac{dE}{dt}=3.6\times {10}^{26}{\text{Js}}^{-1}$

Also, we know that, $c=3\times {10}^8{\text{ms}}^{-1}$

$\Rightarrow 3.6\times {10}^{26}=\left(\frac{dm}{dt}\right)(3\times {10}^8{)}^2$

$\Rightarrow \frac{dm}{dt}=\frac{36}{9}\times {10}^9=4\times {10}^9{\text{kgs}}^{-1}$

Hence, option $\left(D\right)$ is correct.