Question

What is the potential energy of an object of mass \( m \) placed on the surface of the Earth? (Mass of Earth = \( M \), radius of Earth = \( R \))

• A. \( -\frac{GMm}{R} \)
• B. \( \frac{GMm}{R^2} \)
• C. \( -\frac{GMm}{R^2} \)
• D. \( \frac{GMm}{R} \)

Hint:

The potential energy of an object near the surface of the Earth is negative because the gravitational force is attractive, and we take the reference point of zero potential energy at infinity.

Answer 1

The Correct Option is A

The potential energy \( U \) of an object of mass \( m \) placed at a distance \( R \) from the center of the Earth (i.e., on the surface of the Earth) is given by the gravitational potential energy formula: \[ U = -\frac{GMm}{R} \] Where: - \( G \) is the gravitational constant, - \( M \) is the mass of the Earth, - \( m \) is the mass of the object, - \( R \) is the radius of the Earth. Thus, the correct answer is: \[ \boxed{(A) \, -\frac{GMm}{R}} \]