Q. The mean radius of the earth’s orbit round the sun is $1.5 \times 10^{11}$. The mean radius of the orbit of mercury round the sun is $6 \times 10^{10}m$. The mercury will rotate around the sun in
A) A year
B) Nearly 4 years
C) Nearly $\frac{1}{4}$ year
D) 2.5 years
Explanation
(c) $\frac{T_{mercury}}{T_{earth}} = \left( \frac{r_{mercury}}{r_{earth}} \right)^{3/2} = \left( \frac{6 \times 10^{10}}{1.5 \times 10^{11}} \right)^{3/2} = \frac{1}{4}$
(approx.)
$\therefore T_{mercury} = \frac{1}{4}year$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.