\[
\left\{\begin{array}{cccc}
N_{av}=1400\,\rm{rpm} \\
\Delta E_{max}=1150\,\rm{kg\cdot cm} \times 9.81\,\rm{m/s^2} \\
\delta_f=0.01 \\
\kappa =0.15\,\rm{m}
\end{array}\right.
\]
\[
\begin{align}
J
&=\frac{1150 \times 10^{-2}\,\rm{kg \cdot m} \times 9.81 \,\rm{m/s^2}}{0.01 \times \left(\frac{2\pi \times 1400\,\rm{rpm}}{60}\right)^2} \\
&=0.5248\,\rm{kg\cdot m^2}
\end{align}
\]
\[
J=m\cdot \kappa^2\ より \\
\\
\begin{align}
m
&=\frac{J}{\kappa ^2} \\
&=\frac{0.5248\,\rm{kg\cdot m^2}}{(0.15\,\rm{m})^2} \\
&=23.32\,\rm{kg}
\end{align}
\]
\[
\therefore
m=23.3 \ \,\rm{kg}
\]