Question

If the force of gravitational between the earth and a body of mass $M$ on its surface $9\times {10}^{7}N$, what would be the value of $M$. Mass of the earth $=6\times {10}^{24}kg$

• A. $9.2\times {10}^{3}kg$
• B. $9.2\times {10}^{5}kg$
• C. $9.2\times {10}^{6}kg$
• D. $9.2\times {10}^{9}kg$

Answer 1

The correct option is C $9.2\times {10}^{6}kg$

Given,

Mass of earth $M_1=6\times {10}^{24}kg$

Mass of the body $M_2=M$

Force, $F=9\times {10}^{7}N$

universal gravitational constant, $g=6.67\times {10}^{-11}N{m}^2/k{g}^2$

Radius of earth $=6.4\times {10}^6$ m

We know that,

$\begin{array}{c}F=\frac{g{M}_1{M}_2}{R^2}\\ \Rightarrow 9\times {10}^7=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}\times M}{{\left(6.4\times {10}^6\right)}^2}\\ M=9.2\times {10}^{6}kg\end{array}$

Hence, Option $C$ is correct.