The final velocity will be [tex]\rm V= \sqrt{\frac{4gh}{3} }\ m/sec[/tex]. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The change of distance with respect to time is defined as speed.
From the law of conservation of energy:
[tex]\rm KE_i + PE_i = KE_f+PE_f \\\\ 0+mgh = \frac{1}{2} mV^2 +\frac{1}{2} I\omega^2[/tex]
The moment of inertia of the disc;
[tex]\rm I= mr^2[/tex]
It can also be found as;
[tex]\rm I = \frac{V}{r} \\\\[/tex]
Put the obtained values;
[tex]mgh = \frac{1}{2} mv^2+\frac{1}{2} mv^2=mv^2\\\\ mgh = mv^2 \\\\ v=\sqrt{gh}[/tex]
if a disk of the same mass and radius as the hoop rolled down the hill;
[tex]mgh= \frac{1}{2} M+\frac{mr^2}{2r^2} V^2 \\\\ gh = \frac{3}{4} V^2 \\\\ V= \sqrt{\frac{4gh}{3} }\ m/sec[/tex]
Hence the final velocity will be [tex]\rm V= \sqrt{\frac{4gh}{3} }\ m/sec[/tex].
To learn more about the velocity refer to the link;
https://brainly.com/question/862972
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