JAMB Physics 2024 Paper

Concept:Newton's law of universal gravitation states that the gravitational force between two masses is inversely proportional to the square of the distance between them.Explanation:The law is given by $F = \dfrac{Gm_1m_2}{r^2}$.Here, $m_1 = 10^{24}\,\mathrm{kg}$, $m_2 = 10^{27}\,\mathrm{kg}$, $F = 6.67\,\mathrm{N}$, and $G = 6.6 \times 10^{-11}\,\mathrm{Nm^2kg^{-2}}$.Substitute these values into the formula:$$6.67 = \frac{(6.6 \times 10^{-11})(10^{24})(10^{27})}{r^2}$$Simplify the numerator:$$6.67 = \frac{6.6 \times 10^{40}}{r^2}$$Rearrange to solve for $r^2$:$$r^2 = \frac{6.6 \times 10^{40}}{6.67} \approx 9.89 \times 10^{39}$$Take the square root:$$r = \sqrt{9.89 \times 10^{39}} \approx 9.94 \times 10^{19}\,\mathrm{m}$$This is approximately $1.0 \times 10^{20}\,\mathrm{m}$.Answer:A. $1.0 \times 10^{20}\,\mathrm{m}$