Question

A uniform solid sphere of mass \( M \) and radius \( a \) is surrounded by a concentric uniform thin spherical shell of mass 0.5M and radius 1.5a. The gravitational potential energy of a unit mass kept at a distance of 2.5a from the center is:

• A. \( \frac{-3GM}{5a} \)
• B. \( \frac{GM}{5a} \)
• C. \( \frac{2GM}{5a} \)
• D. \( \frac{-2GM}{5a} \)

Hint:

When calculating the gravitational potential energy of a system, consider the contributions from each part of the system separately and apply the superposition principle.

Answer 1

The Correct Option is A

The gravitational potential energy at a point outside the system is the sum of the potentials due to both the sphere and the shell. After calculating the potential energies and applying the principle of superposition, we find the correct value to be \( \frac{-3GM}{5a} \). Thus, the correct answer is option (1).