Explanation

(a) The earth behaves for all external points as if its mass $M$ were concentrated at its centre. When man of mass$\ m$ walks from a point on earth’s surface and reaches diagonally opposite point, then gravitational potential energy given by
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ U = - \frac{GMm}{R}$
Will remain same.
Hence, no work is done by the man against gravity.