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A horizontal disc rotating freely about a vertical axis makes 100rpm.A small piece of wax of mass 10kg falls vertically on the disc and adheres to it at a distance of 9cm from the axis.If the number of revolutions per minute is thereby reduced to 90.Calculate the moment of inertia of disc.

A horizontal disc rotating freely about a vertical axis makes 100rpm.A small piece of wax of mass 10kg falls vertically on the disc and adheres to it at a distance of 9cm from the axis.If the number of revolutions per minute is thereby reduced to 90.Calculate the moment of inertia of disc.

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

taking wax & disk as a system ....

then there is no external torque acting on this system so angular momentam will remain conserved..

IW = IfWf              ..............1

finally moment of inertia = I + Iwax

Iwax = mr2 =  10(9*10-2)2                                         (r = 9cm = 9*10-2m  &   m =10kg )

                = 0.081 kg-m2

If = I + 0.081           ..........2

putting 2 in 1

 IW = (I+0.081)Wf

 W/Wf = (1+.081/I)                                 {W = 100rpm &  Wf=90rpm (given)}

 100/90 = 1 + 0.081/I

  I = 0.729kg-m2

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