Question

A luminous body radiates energy at a rate $3.6 \times 10^{28}$ J/s, then loss of mass of the body per second is

• A. $2 \times 10^3 \, kg / s$
• B. $3 \times 10^4 \, kg / s$
• C. $4 \times 10^{11} \, kg / s$
• D. $5 \times 10^5 \, kg / s$

Answer 1

Answer: (C)

Energy and mass are related by the relation
$ E = mc^2$
Differentiating, we get
$ \frac{dE}{dt} = m \times [0] + c^2 \, \frac{dm}{dt}$
$\Rightarrow 3.6 \times 10^{28} = 9 \times 10^{16} \, \frac{dm}{dt}$
$\Rightarrow \frac{dm}{dt} = 4 \times 10^{11} \, kg/s$