Question

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

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

Answer 1

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

We have,

mass of earth(m)$=6\times {10}^{24}$kg

angular velocity $\left(\omega \right)=2\times {10}^{-7}$ $\frac{rad}{s}$

Radius$\left(R\right)=1.5\times {10}^8$km

$=1.5\times {10}^{11}$m

Since, the earth is revolving in circular orbit given in question. So, there will be centripetal force($F_c$) exerted by the sun.

$F_c=mR{\omega }^2$

$=6\times {10}^{24}\times 1.5\times {10}^{11}\times (2\times {10}^{-7}{)}^2$

$=9\times {10}^{35}\times 4\times {10}^{-14}$

$F_c=36\times {10}^{21}$N.