Gravitational Field and Potential for System of Masses – Rankers Physics
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Gravitational Field and Potential for System of Masses

Assertion (A): For a system of masses at some finite distance, gravitational field can be zero but gravitational potential can not be zero. Reason (R): Gravitational field is a scalar quantity while gravitational potential is a vector quantity.
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true. Gravitational field is a vector quantity, so fields from multiple masses can cancel out at certain points (e.g., between two equal masses). Gravitational potential, being a scalar sum of negative values \( V = \sum ( -\frac{Gm_i}{r_i}) \) for positive masses, can never be zero at a finite distance (only at infinity). Reason (R) is false. Gravitational field is a vector quantity, while gravitational potential is a scalar quantity. Thus, (A) is true but (R) is false.

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