Why is no work done when you hold a book in place over your head?
a a force is applied to the book, but there is no movement.
b the book has motion, but no force is applied to it.
c a force is applied to the book, causing it to move.

The answer would be A). The reason for this is that one of the formula for work is W = F x d. Since there is no movement in terms of distance (d). Then the total work done would also be zero. Anything times zero would be zero (generally, there are some wierd math exceptions).

If you want to analyze this further, there is an upward normal force that is pushing the book up and there is also an equal but opposite gravitational force pushing it down since there is no movement. Since both these forces (no other external forces) hold the book stationary in its place (no movement while these forces are being applied) then the work done for the book as a whole is zero.

It will be A since a force is being applied but it won’t move