Answer with Explanation:
We are given that
Diameter=d=22.6 cm
Mass,m=426 g=[tex]426\times 10^{-3} kg[/tex]
1 kg=1000 g
Radius,r=[tex]\frac{d}{2}=\frac{22.6}{2}=11.3 cm=11.3\times 10^{-2} m[/tex]
1m=100 cm
Height,h=5m
[tex]I=\frac{2}{2}mr^2[/tex]
a.By law of conservation of energy
[tex]\frac{1}{2}I\omega^2+\frac{1}{2}mv^2=mgh[/tex]
[tex]\frac{1}{2}\times \frac{2}{3}mr^2\omega^2+\frac{1}{2}mr^2\omega^2=mgh[/tex]
[tex]v=\omega r[/tex]
[tex]gh=\frac{1}{3}r^2+\frac{1}{2}r^2=\frac{5}{6}r^2\omega^2[/tex]
[tex]\omega^2=\frac{6}{5r^2}gh[/tex]
[tex]\omega=\sqrt{\frac{6gh}{5r^2}}=\sqrt{\frac{6\times 9.8\times 5}{5(11.3\times 10^{-2})^2}}=67.86 rad/s[/tex]
Where [tex]g=9.8m/s^2[/tex]
b.Rotational kinetic energy=[tex]\frac{1}{2}I\omega^2=\frac{1}{2}\times \frac{2}{3}mr^2\omega^2=\frac{1}{2}\times \frac{2}{3}(426\times 10^{-3})(11.3\times 10^{-2})^2(67.86)^2=8.35 J[/tex]
Rotational kinetic energy=8.35 J
