Two bodies of masses 2 kg and 8 kg are at rest. The ratio of times for which the same force must act on them to generate the same K.E in both of them is

${\mathrm{m}}_1=2 \mathrm{kg} {\mathrm{m}}_2=8 \mathrm{kg}$
Kinetic energy of 2 kg body = kinetic energy 8 kg body
$\frac{1}{2}{\mathrm{m}}_1{\mathrm{v}}_1^2=\frac{1}{2}{\mathrm{m}}_2{\mathrm{v}}_2^2$
$$\begin{gathered} \frac{{\mathrm{v}}_1^2}{{\mathrm{v}}_2^2}=\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}=\frac{8}{2} \\ \frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}=\frac{2}{1} \\ \frac{{\mathrm{at}}_1}{{\mathrm{at}}_2}=\frac{2}{1} \\ \frac{\frac{\mathrm{F}}{{\mathrm{m}}_1}{\mathrm{t}}_1}{\frac{\mathrm{F}}{{\mathrm{m}}_2}{\mathrm{t}}_2}=\frac{2}{1} \\ \frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}\times \frac{2}{1} \\ \frac{{\mathrm{t}}_1}{{\mathrm{t}}_2}=\frac{2}{8}\times \frac{2}{1} \\ {\mathrm{t}}_1:{\mathrm{t}}_2=1 :2 \end{gathered}$$