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

Gravitational Potential Energy: Practice Problem & Solution

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

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Gravitational Potential Energy. Understanding the underlying formula is key to arriving at the correct answer below:

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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