A disk and a hoop (bicycle wheel) of equal radius and mass each have a string wr

Question

A disk and a hoop (bicycle wheel) of equal radius and mass each have a string wrapped around their circumferences Hanging from the strings, halfway between the disk and the hoop, is a block of mass m, as shown in the fiqure(Fiqure 1) The disk and the hoop are free to rotate about their centers. When the block is allowed to fall does it stay on the center line, move toward the right, or move toward the left? Choose the best explanation from among the following The disk is harder to rotate and hence its angular acceleration is less than that of the wheel. The system is symmetric with equal mass and radius on either side The wheel has the greater moment of inertia and unwinds more slowly than the disk.

Explanation / Answer

PART A)

move towards left

Explanation :

The moment of inertia of hoop = MR^2

and the moment of inertia of disk = 0.5*MR^2

As the moment of inertia of hoop is greater than disk, so the angular acceleration of hoop is less than that of the disk and thus due to this mismatch of angular accelerations, the body will move towards the hoop and away from the disk.

B)

Option 3 is correct:

as explained above in part A)

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