question_answer

The earth of mass 6 xl024 kg revolves around the sun with an angular velocity of \[2\times {{10}^{-7}}\] rad/s. In a circular orbit of radius \[1.5\times {{10}^{8}}\] km, the force exerted by the sun, on the earth is :

A)  \[27\times {{10}^{39}}N\]

B)  \[36\times {{10}^{21}}N\]

C)  \[18\times {{10}^{25}}N\]

D) \[6\times {{10}^{19}}N\]

Correct Answer: B

Solution :

Key Idea: Earth is acted upon by a centripetal force directed towards the sun. On the basis of Keplers law, Newton drew the following conclusion that planet is acted upon by a centripetal force directed towards the sun. Force is given by                 \[F=\frac{m{{v}^{2}}}{r}\] where v is velocity and r is the radius. Also,      \[v=r\omega \] \[\therefore \] \[F=mr{{\omega }^{2}}\] Putting the numerical values, we have                 \[F=(6\times {{10}^{24}})\times (1.5\times {{10}^{11}})\times {{(2\times {{10}^{-7}})}^{2}}\]                 \[=36\times {{10}^{21}}N\] Note: This force is attractive in nature.