Q. Sun is about 330 times heavier and 100 times bigger in radius than earth. The ratio of mean density of the sun to that of earth is
A) $3.3 \times 10^{- 6}$
B) $3.3 \times 10^{- 4}$
C) $3.3 \times 10^{- 2}$
D) $1.3$
Explanation
(b) As mass, $M = \frac{4}{3}\pi R^{2}\rho$
or $\rho = \frac{3M}{4\pi R^{3}}$
$\therefore\frac{\ \rho_{s}}{\ \rho_{s}} = \frac{M_{s}}{M_{e}} \times \frac{R_{e}^{3}}{R_{s}^{3}} = 330 \times \left( \frac{1}{100} \right)^{3} = 3.3 \times 10^{- 4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.