TORQUE of disks!!!!!?

Three flat disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk consists of the same two materials, one denser than the other (density is mass per unit volume). In disks 1 and 3, the denser material forms the outer half of the disk area. In disk 2, it forms the inner half of the disk area. Forces with identical magnitudes are applied tangentially to the disks, at the outer edge of disks 1 and 2 and at the interface of the two materials for disk 3





(a) Rank the disks according to the torque about the disk center, greatest first (use only the symbols %26gt; or =, for example, 1=2%26gt;3).


(b) Rank the disks according to the rotational inertia about the disk center, greatest first (use only the symbols %26gt; or =, for example, 1=2%26gt;3).


(c) Rank the disks according to the angular acceleration of the disk, greatest first (use only the symbols %26gt; or =, for example, 1=2%26gt;3).

TORQUE of disks!!!!!?
Torque is defined as the product of tangential force and the dist. of its application point from the centre, so it is in the same ratio as the latter


(a) 1=2%26gt;3


The rotational inertia of disk two will be least because the denser material is closer to the centre so


(b) 1=3%26gt;2


we know, Torque = Moment of Inertia * Ang. acceleration.


so α = T / I


Torque of 1 and 3 are in the ratio √2 and their I are equal. so α for 1 is lesser. Also T for 1 and 2 is equal and I for 1 is higher so α for 1 is less. But the relation between 3 and 2 cannot be said until the relation between the densities of the materials is not provided. we can only say that


(c) 3%26gt;1%26lt;2