A body of mass $m=10^{−2}\; kg$ is moving in a medium and experiences a frictional force $F=−kv^2$. Its initial speed is $v_0=10 ms^{−1}$. If, after $10\;s$, its energy is $\large\frac{1}{8}$$ \;mv_0^2$,the value of k will be :

Question

$\begin{array}{1 1}(1) 10^{-3} \;kg m^{-1} \\ (2) 10^{-3} \;kg s^{-1} \\ (3) 10^{-4} \;kg m^{-1} \\ (4) 10^{-1} \;kg m^{-1} s^{-1} \end{array} $