The depth at which acceleration due to gravity becomes g n is ( R = radius of earth, g = acceleration due to gravity) ( n = integer)

Step-by-step solution

The acceleration due to gravity at depth d below Earth's surface is given by g' = g (1 - d R ) . Since g' = g n , substitution yields g n = g (1 - d R ) . Dividing both sides by g and simplifying produces d R = 1 - 1 n = n-1 n . The depth is therefore d = R n-1 n , which corresponds to option A .