Solution:

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).