# Two discs  and  are mounted coaxially on a vertical axle. The discs have moments of inertia  and  respectively about the common axis. Disc  is imparted an initial angular velocity  using the entire potential energy of a spring compressed by a distance . Disc  is imparted an angular velocity  by a spring having the same spring constant and compressed by a distance . Both the discs rotate in the clockwise direction The loss of kinetic energy during the above process is a) b) c) d)

## Question ID - 101407 :- Two discs  and  are mounted coaxially on a vertical axle. The discs have moments of inertia  and  respectively about the common axis. Disc  is imparted an initial angular velocity  using the entire potential energy of a spring compressed by a distance . Disc  is imparted an angular velocity  by a spring having the same spring constant and compressed by a distance . Both the discs rotate in the clockwise direction The loss of kinetic energy during the above process is a) b) c) d)

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(b)

Loss of kinetic energy

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The general motion of a rigid body can be considered to be a combination of (i) a motion---centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through centre of mass. These axes need not be stationary. Consider, for example, a thin uniform welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure. Where disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed , the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass the disc about the -axis, and (ii) a rotation of the disc through an instantaneous vertical axis pass through its centre of mass (as in seen from the changed orientation of points  and ). Both the motions have the same angular speed  in the case

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 Which of the following statement regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct a) It is  for both the cases b) It is  for case ; and  for case c) It is  for case ; and  for case d) It is  for both the cases