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A metal rod of length ‘L’ and mass ‘m’ is pivoted at one end. A thin disk of mass ‘M’ and radius ‘R’ is attached at its center to the free end of the rod. Consider two ways the disc is attached : (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true? (JEE 2011) (A) Restoring torque in case A = Restoring torque in case B. (B) Restoring torque in case A Resorting torque in case B. (C) Angular frequency for case A Angular frequency for case B. (D) Angular frequency for case A Angular frequency for case B. The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass. These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed ω, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q). Both these motions have the same angular speed ω in this case Advanced problems Playlist • Advanced Level Physics Problems For IIT JE... JEE Main Revision Problems, JEE Main Specific Topics, JEE Main previous Year Questions Playlist • JEE Main Special Topics theory Lectures, R... Pathfinder Physics Solutions Playlist • Pathfinder Physics Solutions IRODOV Solutions Playlist • Irodov Solutions Toppling Roatational Mechanics Playlist • Toppling | Rotational Mechanics | Theory &... Instantaneous Axis of Rotation playlist • Instantaneous Axis Of Rotation : Theory & ... Center of Mass Frame Playlist • Centre of Mass frame Theory & Examples for... Physics Concept Videos for IIT JEE Advanced and Main, NEET • Physics Concept Videos useful for IIT JEE Theory Videos GEOMETRICAL OPTICS • Geometrical Optics : Reflection From Plane... • Geometrical Optics : Spherical Mirror : Th... • Geometrical Optics : Refraction From Plane... • Geometrical Optics : Refraction by Spheric... • Geometrical Optics : Prism, Dispersion & A... ELECTROSTATICS • Electrostatics : Coulomb's law, Electric F... • Electric Flux & Gauss Law : Theory Lecture... GRAVITATION • Gravitation : Theory Lectures for IIT JEE ... CAPACITORS • Capacitors : Theory Lectures for IIT JEE P... MAGNETIC FORCE • Magnetic Force : Theory Lectures for IIT J... MAGNETIC EFFECTS OF CURRENT • Magnetic Effects Of Current : Theory Lectu...