Rankers Physics

Gravitational Potential: Practice Problem & Solution

Infinite number of bodies, each of mass $2 \text{ kg}$ are situated on x-axis at distances $1 \text{ m}$, $2 \text{ m}$, $4 \text{ m}$, $8 \text{ m}$, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be: (2013)
$-4G$
$-G$
$-\frac{8}{3}G$
$-\frac{4}{3}G$

Solution Explained:

To solve this problem, we apply the core principles of Gravitational Potential. Understanding the underlying formula is key to arriving at the correct answer below:

Total potential $V = -GM \sum \frac{m}{r} = -2G (1 + \frac{1}{2} + \frac{1}{4} + ...) = -2G \times \frac{1}{1 - 0.5} = -4G$.

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