a$.$ No$,$ the merry$-$go$-$round will have angular momentum in one direction and he in the other, they

will cancel and he$$ll stay right above the book.

b$.$ No$,$ because the initial angular momentum is zero, so the final must be zero too, causing his

angular velocity to be zero, so he$$ll stay right above the book.

c$.$ Yes, angular momentum is not conserved so he$$ll move around away from the book.

d$.$ Yes, because his moment of inertia is smaller than the merry$-$go$-$round$$s$,$ so his angular velocity

will be bigger, so he$$ll move around away from the book