$(a)$ Can a body have energy without having momentum? Explain.
$(b)$ Can a body have momentum without having energy? Explain.

(N/A) Yes,a body at rest has no momentum,i.e.,$p = 0$. However,it can possess potential energy $(U)$ due to its position or configuration. Therefore,its total energy $E = K + U = U$ is not zero. For example,a stone lying on a roof or a wound-up spring of a clock.
$(b)$ No,a body cannot have momentum without having energy. Momentum $(p = mv)$ implies that the body is in motion $(v \neq 0)$. If a body is in motion,it must possess kinetic energy $(K = \frac{1}{2}mv^2)$. Since kinetic energy is a component of total energy,a body with momentum must possess energy.