Answer:
Height will be 3.8971 m
Explanation:
We have given that radius of the solid r = 1.60 m
Mass of the solid disk m = 2.30 kg
Angular velocity [tex]\omega =4.46rad/sec[/tex]
Moment of inertia is given by [tex]I=\frac{1}{2}mr^2[/tex]
Transnational Kinetic energy is given by [tex]KE=\frac{1}{2}mv^2[/tex] as we know that v = [tex]v=\omega r[/tex]
So [tex]KE=\frac{1}{2}m(\omega r)^2[/tex]
Rotational kinetic energy is given by [tex]KE_{ROTATIONAL}=\frac{1}{2}I\omega ^2=\frac{1}{2}\left ( \frac{1}{2}mr^2 \right )\omega ^2=\frac{1}{4}m(r\omega )^2[/tex]
Potential energy is given by mgh
According to energy conservation
[tex]mgh=\frac{1}{2}m(\omega r)^2+\frac{1}{4}m(\omega r)^2[/tex]
[tex]h=\frac{3r^2\omega ^2}{4g}=\frac{3\times 1.60^2\times 4.46^2}{4\times 9.8}=3.8971m[/tex]
