Centre of Mass and Gravity at Earth’s Centre – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

Assertion (A): At the centre of the earth, a body has centre of mass, but no centre of gravity. Reason (R): Acceleration due to gravity is zero at the centre of the earth.  
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 Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. A body always has a center of mass.

Centre of gravity is the point where the net gravitational torque is zero. At the center of the Earth, the acceleration due to gravity \( g \) is zero. Thus, there is no gravitational force, and consequently, no center of gravity in the usual operational sense.

Reason (R) is true. The acceleration due to gravity \( g \) is indeed zero at the centre of the earth. Since the absence of gravity leads to no definable centre of gravity, (R) is the correct explanation for (A).

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