A circular disc of mass M and radius R is rotating about its axis with angular speed ω$$1$$. 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 ω$$2$$. The energy lost in the process is p% of the initial energy. Value of p is $$__________$$ .

Question

A circular disc of mass M and radius R is rotating about its axis with angular speed  ω$$1$$. 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  ω$$2$$. The energy lost in the process is p% of the initial energy. Value of p is $$__________$$ .

Infinity Learn · Accepted Answer

Conservation of Angular Momentum, ​$$MR22$$ω$$1=MR22+MR242$$ω$$2$$​⇒ω$$2=45$$ω$$1Given$$ : energy $$lost=p$$% of initial energy​⇒Ki−$$Kf=p100$$×Ki⇒$$p=Ki$$−KfKi×$$100$$ $$=$$ $$12MR22$$ω$$12$$−$$12MR22+MR242$$ω$$2212MR22$$ω$$12$$×$$100$$⇒$$p=1$$−$$54$$ω$$2$$ω$$12$$×$$100$$​⇒$$p=1$$−$$45$$×$$100=20$$

Rotational motion

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Rotational motion

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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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