A uniform dick, a thin hoop, and a uniform sphere, all with the same mass outer
ID: 2018748 • Letter: A
Question
A uniform dick, a thin hoop, and a uniform sphere, all with the same mass outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rime, as shown. Rank the objects according the their angular velocities after a given time t, least to greatest.
A)disk, hoop, sphere
B)hoop, disk, sphere
C)hoop, sphere, dick
D)hoop, dick, sphere
E)sphere, dick, hoop
Explanation / Answer
Data: Hoop, disk, sphere --> Same mass, radius Initial angular velocity, i = 0 Force on each = F Time = t Let Radius of each = r Solution: Moment of inertia of disk, I1 = m r^2 /2 = 0.5 mr^2 Moment of inertia of joop, I2 = m r^2 Moment of inertia of sphere, I3 = (2/5) mr^2 = 0.4 mr^2 f = i + t = 0 + ( / I ) t = ( F r / I ) t Hence, f is inversely proportional to moment of inertia. Order of I ( least to greatest ) : I3 (sphere) , I1 (disk) , I2 (hoop) , , Order of f: ( least to greatest) This order is opposite to that of moment of inertia hoop, disk, sphere Ans: Option - dRelated Questions
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