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(a) Show that a solid cylinder of mass M and radius R is equivalent to a thin hoop of mass M and radius R/√2, for rotation about a central axis. (b) The radial distance from a given axis at which the mass of a body could be concentrated without altering the rotational inertia of the body about that axis is called the radius of gyration. Let k represent the radius of gyration and show that This gives the radius of the “equivalent hoop” in the general case.

(a) Show that a solid cylinder of mass M and radius R is equivalent to a thin hoop of mass M and radius R/√2, for rotation about a central axis. (b) The radial distance from a given axis at which the mass of a body could be concentrated without altering the rotational inertia of the body about that axis is called the radius of gyration. Let k represent the radius of gyration and show that
                                                    
This gives the radius of the “equivalent hoop” in the general case.

Grade:upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
8 years ago
233-1422_1.PNG
Therefore, the rotational inertia of the hoop of radius 233-23_1.PNGabout the cylinder axis is equal to the rotational inertia of the solid cylinder.
(b) The rotational inertia of the rigid body is given as:

233-283_1.PNG

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