Answer:
The disk will reach the bottom first.
Explanation:
As we know:
change in kinetic energy = change in potential energy
ΔK.E = -ΔP.E
[tex]\frac{1}{2} mv^{2} + \frac{1}{2}Iw^{2} = Mgh[/tex]
[tex]Mv^{2} +I\frac{v^{2} }{R^{2} } = 2Mgh[/tex]
[tex]v=\sqrt{\frac{2Mgh}{M+\frac{I}{R^{2} } } }[/tex]
For the disk:
[tex]I=\frac{MR^{2} }{2}[/tex]
For Hoop:
[tex]I=MR^{2}[/tex]
Hence
Velocity for the disk:
[tex]v=\sqrt{\frac{4}{3}gh }[/tex]
Velocity for the Hoop:
[tex]v=\sqrt{gh}[/tex]
