Question

The earth takes approximately 365.25 days to revolve around the sun, if the approximate distance between the earth and the sun is $149.6\times {10}^{6}km$. Find the force acting on earth.
[Assume mass of earth $=5.97\times {10}^{24}kg$]

• A. $3.54\times {10}^{12}N$
• B. $3.54\times {10}^{2}N$
• C. $9.54\times {10}^{22}N$
• D. $3.54\times {10}^{22}N$

Answer 1

The correct option is D $3.54\times {10}^{22}N$

Given:

time = $365.25days$ = $31557600s$

radius = $149.6\times {10}^{9}m$

mass = $5.97\times {10}^{24}kg$

Force = $\frac{m{v}^2}{r}$

$\Rightarrow$F = $\frac{m{\left(\frac{2\pi r}{t}\right)}^2}{r}$

$\Rightarrow$F = $\frac{4m{\pi }^{2}r}{t}$

On substituting the values we get

F = $3.54\times {10}^{22}N$