Question

Find ratio of potential energy of a body at point A to point B for the figure shown. 

• A. \(1:3\)
• B. \(2:3\)
• C. \(3:1\)
• D. \(1:2\)

Hint:

Gravitational potential energy varies as: \[ U \propto -\frac{1}{r} \] If distance triples, potential energy becomes one-third.

Answer 1

The Correct Option is C

Concept: Gravitational potential energy of a body: \[ U = -\frac{GMm}{r} \] where \(r\) is the distance from the center of the earth.
Step 1: Distance of point A from Earth's centre. From the diagram, \[ r_A = R \]
Step 2: Distance of point B from Earth's centre. Point B is \(2R\) above A. \[ r_B = R + 2R \] \[ r_B = 3R \]
Step 3: Find ratio of potential energies. \[ U_A = -\frac{GMm}{R} \] \[ U_B = -\frac{GMm}{3R} \] \[ \frac{U_A}{U_B} = \frac{-\frac{GMm}{R}}{-\frac{GMm}{3R}} \] \[ \frac{U_A}{U_B} = 3 \] \[ \boxed{U_A : U_B = 3:1} \]