Answer
$(a)\space P = (\frac{M}{2}+m)Va$
$(b)\space 1.1\%$
$(c)\space 0.28\%$
Work Step by Step
Please see the image below.
(a) Let's apply equation $V=u +at$
$\rightarrow V=u+at$
$V=0+at$
$V=at-(1)$
Let's apply the equation of conservation of kinetic energy.
Total kinetic energy = Linear kinetic energy + Rotational kinetic energy
$E=\frac{1}{2}MV^{2}+\frac{1}{2}I\omega^{2}\times4-(2)$
$E=\frac{1}{2}MV^{2}+2I\omega^{2}$
For a solid disk,
$I=\frac{1}{2}MR^{2}-(3)$
$(3)=\gt (2)$
$E=\frac{1}{2}MV^{2}+\frac{1}{2}mR^{2}\times\frac{V^{2}}{R^{2}}=V^{2}(\frac{M}{2}+m)-(3)$
Rate of change in kinetic energy = E - 0 = E
Power (P) $=\frac{E}{t}$
$(3)=\gt P=\frac{V^{2}}{t}(\frac{M}{2}+m)=V\times \frac{V}{t}(\frac{M}{2}+m)$
$(1)=\gt P=Va(\frac{M}{2}+m)$
(b) Reduce the mass by 10 kg from non-rolling parts,
$P_{1}=Va[\frac{(M-10)}{2}+m]=Va(\frac{M}{2}+m)-10Va$
$P_{1}=P-10Va$
Percentage of power decrease $= \frac{P-P_{1}}{P}\times 100\%$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space=\frac{10Va}{Va(\frac{M}{2}+m)\times}\times100\%$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space=\frac{1000}{\frac{1780}{2}+15.8}=1.1\%$
(c) Reduce the mass by 10 kg from rolling parts.
$P_{2}=Va[\frac{M}{2}+(m-2.5)]$
$P_{2}=Va[\frac{M}{2}+m]-2.5Va$
$2.5Va=P-P_{2}$
Percentage of power decrease $= \frac{P-P_{2}}{P}\times 100\%$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space=\frac{2.5Va}{Va(\frac{M}{2}+m)\times}\times100\%$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space=\frac{250}{\frac{1780}{2}+15.8}=0.28\%$
