$P=\sqrt{p_x^2+p_y^2}$

$=\sqrt{{\left(2\cos t\right)}^2+{\left(2\sin t\right)}^2}=2$

If $m$ be the mass of the body, then kinetic energy

$=\frac{p^2}{2m}=\frac{{\left(2\right)}^2}{2m}=\frac{2}{m}$

Since kinetic energy does not change with time, both work done and power are zero

Now Power = $Fv\cos \mathrm{\theta }=0$

As $F\ne 0,v\ne 0$

$\therefore \cos \mathrm{\theta }=0$

Or $\mathrm{\theta }=90°$

As direction of $\overrightarrow{\mathrm{p}}$ is same that $\overrightarrow{\mathrm{v}}(\because \overrightarrow{\mathrm{p}}=m\overrightarrow{\mathrm{v}})$ hence angle between $\overrightarrow{\mathrm{F}}$ and $\overrightarrow{\mathrm{p}}$ is equal to $90°$