A space craft from the earth is moving towards the moon, find a location from the earth where at the gravitational force is zero. [Mass of the earth = 6 x 10²⁴ kg, Mass of the moon = 7.4 x 10²² kg, distance between the earth and the moon = 3.8 x 10⁸ m]

$\begin{array}{l}\text { Solution: }(b) ; \frac{G M_{E} m}{x^{2}}=\frac{G M_{M o o n} m}{(d-x)^{2}} \Rightarrow \frac{6 \times 10^{24}}{x^{2}}=\frac{7.4 \times 10^{22}}{(d-x)^{2}} \\ \begin{array}{ll}\Rightarrow \frac{d-x}{x}=\frac{1}{9} \Rightarrow 9 d-9 x=x \Rightarrow 9 d=10 x & \\ \Rightarrow x=\frac{9 d}{10}=\frac{9}{10} \times 3.8 \times 10^{8} \mathrm{~m} & \\ =3.4217 \times 10^{8} \mathrm{~m} & \begin{array}{l}M_{E}=6 \times 10^{24} \mathrm{~kg} \\ M_{\text {Moon }}=7.4 \times 10^{22} \mathrm{~kg} \\ d=3.8 \times 10^{8} \mathrm{~m}\end{array} \end{array}\end{array}$