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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 p% of the initial energy. Value of p is __________ .

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answer is 0020.00.

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Detailed Solution

Conservation of Angular Momentum, MR22ω1=MR22+MR242ω2⇒ω2=45ω1Given : energy lost=p% of initial energy⇒Ki−Kf=p100×Ki⇒p=Ki−KfKi×100 = 12MR22ω12−12MR22+MR242ω2212MR22ω12×100⇒p=1−54ω2ω12×100⇒p=1−45×100=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 p% of the initial energy. Value of p is __________ .