If the kinetic energy of a body is fourtimes its momentum, its velocity is

Given,

Kinetic energy is four times its momentum,

$KE=4P$

We know that,

kinetic energy =$\frac{1}{2}m{v}^2$

momentum $=P=mv$

Thus,

$\mathrm{KE}=\frac{1}{2}\mathrm{mv} \mathrm{v} =\frac{1}{2}\mathrm{pv} (\because \mathrm{p}=\mathrm{mv})$

$$\begin{gathered} \mathrm{Given}, 4\mathrm{P}=\frac{\mathrm{P}}{2}\mathrm{v} \\ \Rightarrow \mathrm{v}=4\times 2=8\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence the correct answer is 8m/s.