Question

The potential energy of a satellite of mass \( m \) revolving around the earth at a height of \( R \) from the surface of the earth is:

• A. \( -0.5mgR_e \)
• B. \( -mgR_e \)
• C. \( -2mgR_e \)
• D. \( -4mgR_e \)

Hint:

Gravitational potential energy at a height \(h\) is given by \( U = - \frac{GMm}{R + h} \). If the height is equal to the radius of the earth, the potential energy becomes \( -0.5mgR_e \).

Answer 1

The Correct Option is A

The gravitational potential energy of a satellite at height \(h\) is given by: \[ U = - \frac{GMm}{R + h}. \] Here \( R \) is the radius of the earth, and \( h = R \). Substituting \(h = R\) into the formula: \[ U = - \frac{GMm}{2R}. \] Since \(GM = g R^2\), the potential energy becomes: \[ U = -0.5mgR_e. \]