Gravitational Potential: Practice Problem & Solution
Assertion (A): Assuming zero potential at infinity, the gravitational potential at a point can never be positive. Reason (R): The magnitude of gravitational force between two particles has inverse square dependence on the distance between two particles.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Gravitational Potential. Understanding the underlying formula is key to arriving at the correct answer below:
Assertion (A) is true. For physical masses (which are always positive), gravitational potential is given by \( V = -\frac{GM}{r} \). Since G, M, and r are positive, V must always be negative (or zero at infinity). Reason (R) is true. The gravitational force follows Newton's inverse square law, \( F = \frac{GMm}{r^2} \). This inverse square law, combined with the attractive nature of gravity, ensures that the potential energy and thus the gravitational potential remain negative when potential at infinity is set to zero. Thus, (R) is the correct explanation for (A).
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