Question 13: Gravitational Potential and Field at Earth’s Centre – Rankers Physics
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Question 13: Gravitational Potential and Field at Earth’s Centre

Assertion (A): Gravitational potential energy of any mass particle may not be zero at earth centre. Reason (R): Gravitational field intensity at earth centre is zero.
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 potential at the center of a uniform solid sphere is finite (e.g., \( -frac{3}{2} frac{GM}{R} \)), hence potential energy is non-zero. Reason (R) is true. Due to symmetry, the net gravitational field at the Earth's center is zero. However, zero field does not directly explain non-zero potential energy. Thus, (R) is not the correct explanation of (A).

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