Question

An object of mass \( m \) with non-zero angular momentum \( \ell \) is moving under the influence of gravitational force of a much larger mass (ignore drag). Which of the following statement(s) is (are) correct?

• A. If the total energy of the system is negative, then the orbit is always circular.
• B. The motion of \( m \) always occurs in a two-dimensional plane.
• C. If the total energy of the system is 0, then the orbit is a parabola.
• D. If the area of the particle’s bound orbit is \( S \), then its time period is \( 2mS/\ell \).

Hint:

The motion of an object under a central force, like gravity, always occurs in a plane, as the angular momentum remains constant.

Answer 1

The Correct Option is B

Step 1: Understanding the motion of the object.
An object under gravitational influence follows a trajectory constrained by its initial conditions. Since the gravitational force is central, the motion occurs in a plane. The statement about total energy being negative or 0 does not necessarily imply circular or parabolic orbits without further analysis.
Step 2: Conclusion.
Thus, the correct answer is option (B).