Q84 / 160 · JIPMER 2004 · Physics
The earth of mass $=6 \times 10^{24} \mathrm{~kg}$ revolves around the sun with an angular velocity of $2 \times 10^{-7} \mathrm{rad} / \mathrm{s}$ in a circular orbit of radius $1.5 \times 10^8 \mathrm{~km}$. The force exerted by the sun on earth is :
- A$6 \times 10^{19} \mathrm{~N}$
- B$18 \times 10^{25} \mathrm{~N}$
- Correct answerC$36 \times 10^{21} \mathrm{~N}$
- D$27 \times 10^{39} \mathrm{~N}$
Solution
Here: Mass of earth $M_e=6 \times 10^{24} \mathrm{~kg}$
Angular velocity of earth $\omega=2 \times 10^{-7} \mathrm{rad} / \mathrm{s}$
Radius of circular orbit
$\begin{aligned}R & =1.5 \times 10^8 \mathrm{~km} \\& =1.5 \times 10^{11} \mathrm{~m}\end{aligned}$
Force exerted on the earth by the sun is given by
$\begin{aligned}F & =M_e R \omega^2 \\& =6 \times 10^{24} \times 1.5 \times 10^{11} \times\left(2 \times 10^{-7}\right)^2 \\& =36 \times 10^{21} \mathrm{~N}\end{aligned}$
Hence, the correct answer is option: 'C'.