(A) Yes,an object can have mechanical energy even if its momentum is zero.
Mechanical energy is the sum of kinetic energy $(KE)$ and potential energy $(PE)$.
Momentum $(p)$ is defined as the product of mass $(m)$ and velocity $(v)$,i.e.,$p = mv$.
If momentum is zero $(p = 0)$,then the velocity of the object must be zero $(v = 0)$.
Since kinetic energy is given by $KE = \frac{1}{2}mv^2$,if $v = 0$,then $KE = 0$.
However,the object can still possess potential energy due to its position or configuration (e.g.,a ball held at a height above the ground).
Therefore,the total mechanical energy $(ME = KE + PE)$ can be non-zero because $PE$ is non-zero.