\(ma = F - f     \)      ...(i)

And, torque \(\tau  = I\alpha \)

\(\begin{array}{l}
\frac{{m{R^2}}}{2}\alpha  = fR\,\\
\,\frac{{m{R^2}}}{2} - \frac{a}{R} = fR\,\,\left[ {\alpha  = \frac{a}{R}} \right]\\
\frac{{ma}}{2} = f\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)
\end{array}\)

Put this value in equation \((i),\)

\(ma = F - \frac{{ma}}{2}\,\,or\,\,F = \frac{{3ma}}{2}\)