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?
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?
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The motion of an object under a central force (like gravity) occurs in a plane due to constant angular momentum. If the total energy is zero, the orbit is parabolic, and the time period is related to the area swept by the object.
Updated On: Dec 15, 2025
- If the total energy of the system is negative, then the orbit is always circular.
- The motion of \( m \) always occurs in a two-dimensional plane.
- If the total energy of the system is 0, then the orbit is a parabola.
- If the area of the particle’s bound orbit is \( S \), then its time period is \( 2mS/\ell \).
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The Correct Option is B, C, D
Solution and Explanation
Step 1: Understanding the motion of the object.
The object under gravitational influence moves in a plane due to the central nature of the gravitational force. This is a well-established result from the conservation of angular momentum. The total energy being negative does not necessarily imply a circular orbit, and the orbit is parabolic if the total energy is zero. The area swept by the object is proportional to the time period, following Kepler's laws. Thus, the time period is \( 2mS/\ell \).
Step 2: Conclusion.
Thus, the correct answers are options (B), (C), and (D).
The object under gravitational influence moves in a plane due to the central nature of the gravitational force. This is a well-established result from the conservation of angular momentum. The total energy being negative does not necessarily imply a circular orbit, and the orbit is parabolic if the total energy is zero. The area swept by the object is proportional to the time period, following Kepler's laws. Thus, the time period is \( 2mS/\ell \).
Step 2: Conclusion.
Thus, the correct answers are options (B), (C), and (D).
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