Question

The gravitational potential energy of a system of two bodies each of mass $m$ and distance $r$ between them is (G = gravitational constant, g = acceleration due to gravity)

• A. $-\frac{Gm^2}{r^2}$
• B. $-\frac{Gm^2}{r}$
• C. $-\frac{gm^2}{r}$
• D. $-G \frac{gm^2}{r}$
• E. $\frac{Ggm}{r^2}$

Hint:

Gravitational potential energy is always negative, indicating an attractive force between masses.

Answer 1

The Correct Option is B

Step 1: The gravitational potential energy ($U$) between two masses $m_1$ and $m_2$ separated by a distance $r$ is given by: \[ U = -\frac{G m_1 m_2}{r} \] Step 2: In this case, both masses are equal to $m$, so the equation simplifies to: \[ U = -\frac{G m^2}{r} \] Step 3: Therefore, the correct answer is (B). \bigskip