Question

The average distance between the earth and the sun is $1.5\times {10}^{11}m$. If the mass of sun is $2\times {10}^{30}kg$ and that of earth is $6\times {10}^{24}kg$, then the force of gravitation between them is:

• A. $3.557\times {10}^{21}N$
• B. $5.357\times {10}^{21}N$
• C. $3.557\times {10}^{22}N$
• D. none of the above

Answer 1

The correct option is C

$3.557\times {10}^{22}N$

Step 1: Given data

Mass of Earth, $m_1=6\times {10}^{24}kg$

Mass of sun, $m_2=2\times {10}^{30}kg$

Distance, $d=1.5\times {10}^{11}m$

Magnitude of force, $F=?$ (To be calculated)

Step 2: Calculating magnitude of force

Applying, $F=\frac{G\times m_1\times m_2}{d^2}$

$$\begin{gathered} \Rightarrow F=\frac{6.67\times {10}^{-11}N{m}^2/k{g}^2\times 6\times {10}^{24}kg\times 2\times {10}^{30}kg}{{(1.5\times {10}^{11}m)}^2} \\ \Rightarrow F=3.557\times {10}^{22}N \end{gathered}$$

Hence, the correct answer is option (C) i.e. $3.557\times {10}^{22}N$