Question

The earth (mass = \[6 \times {10^24}\]kg) revolves around the sun with an angular velocity of \[{\text{2}} \times {\text{1}}{{\text{0}}^{ - 7}}\] rad/s in a circular orbit of radius \[1.5 \times {10^8}\]. The force exerted by the sun on the Earth, in Newtons, is:
(A) \[36 \times {10^{21}}\]
(B) \[27 \times {10^{39}}\]
(C) 0
(D) \[18 \times {10^{25}}\]

Answer 1

Hint The force exerted by the sun on earth is the same as force exerted by earth on sun which is the consequence of Newton’s 3rd law of motion.

Complete step-by-step solution
When an object is moving in a circular path, it experiences a force which is called a centripetal force. This centripetal force pulls the object towards the center of the circle at all times. This centripetal force is given by
\[F = m{\omega ^2}r\]
Where F= centripetal force
M=mass of the moving object
ω= angular velocity of the object
r= distance of the object from the axis of rotation.
Substituting the values given in question,
M=\[6 \times {10^{24}}\]kg
W=\[{\text{2}} \times {\text{1}}{{\text{0}}^{{\text{ - 7}}}}\] rad/s
R=\[1.5 \times {10^8}\]km
F= \[6 \times {10^{24}}\] \[ \times {\text{ (2}} \times {\text{1}}{{\text{0}}^{{\text{ - 7}}}}{)^2}\] \[ \times {\text{ 1}}{\text{.5}} \times {\text{1}}{{\text{0}}^8}\]
F= \[36 \times {10^{21}}\]N

Therefore, the correct answer is option A.

Note This force is centripetal force experienced by earth and it is balanced by the force of gravity between the Earth and the Sun. If there was no centripetal force, Earth would have been pulled inside the sun long ago.