Question

The earth $(\text{mass}=6\times {10}^{24}\text{kg})$ revolves around the sun with an angular velocity of $2\times {10}^{-7}\text{rad/s}$ in a circular orbit of radius $1.5\times {10}^8\text{km}$. The force exerted by the sun on the earth (in Newtons) is

• A. $36\times {10}^{21}$
• B. $27\times {10}^{39}$
• C. Zero
• D. $18\times {10}^{25}$

Answer 1

The correct option is A $36\times {10}^{21}$

Given:
$m=6\times {10}^{24}\text{kg};\omega =2\times {10}^{-7}\text{rad/s}$
$r=1.5\times {10}^8\text{km}=1.5\times {10}^{11}\text{m}$

The force of gravitation exerted by sun provides the necessary centripetal force $=m{\omega }^{2}r$

$\Rightarrow F_g=6\times {10}^{24}\times 4\times {10}^{-14}\times 1.5\times {10}^{11}$

$\Rightarrow F_g=36\times {10}^{21}\text{N}$

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

Key Concept - For uniform spherical masses, gravitational force can be calculated assuming them to be point masses placed at their centers.