A body of mass \(M kg\) is located \(0.5 m\) from a body of mass \(2 M kg\). At the same time, it is \(0.75 m\) from a third body of mass \(3 M kg\) and \(0.9 m\) from a fourth body of mass \(5 M kg\). Which of the three bodies exerts the least gravitational force of attraction on the body of mass \(M kg\) ?
A. 2M kg B. \(3 M kg\) C. \(5 M kg \) D. All forces equal
Correct Answer: B
Explanation
By Newton's law of universal gravitation \begin{aligned} &f=\frac{G m_{1} m_{2}}{r^{2}} \\ &\vec{f}_{1}=\frac{G \times M \times 2 m}{0.5^{2}}=8 G M^{2} \\ &\vec{f}_{2}=\frac{G \times M \times 3 m}{0.75^{2}}=5.33 G M^{2} \\ &\vec{f}_{3}=\frac{G \times M \times 5 m}{0.9^{2}}=6.17 G M^{2} \end{aligned} Thus, body \(2 M kg\) has the greatest and body \(3 M kg\) has the least gravitational force of attraction on the body of mass \(M kg\)
