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Q.

A circular disc of mass M and radius R is rotating about its axis with angular speed ω1. If another stationary disc having radius R2 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2. The energy lost in the process is ρ% of the initial energy. Value of ρ is _________

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answer is 20.

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Detailed Solution

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K=122=122I=L22I

Ii=I1=MR22 ; If=I1+I2=MR22+MR22×4=5MR28

% change in energy =kfkiki×100

=L22MR22L225MR28L22MR22×100=20%

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A circular disc of mass M and radius R is rotating about its axis with angular speed ω1. If another stationary disc having radius R2 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2. The energy lost in the process is ρ% of the initial energy. Value of ρ is _________