A circular disc of mass M and radius R is rotating about its axis with angular speed ω₁. If another stationary disc having radius R/2 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
(Rotational)
A circular disc of mass M and radius R is rotating about its axis with angular speed ω₁. If another stationary disc having radius R/2 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
(Rotational)
Asked by Shiksha User
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1 Answer
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Angular momentum conservation:
⇒ I? ω? + I? ω? = (I? + I? )ωf
⇒ (MR²/2)ω? = (MR²/2 + MR²/8)ωf
⇒ ωf = 4/5 ω?
⇒ KEfinal = ½ (I? + I? )ωf² = (MR²ω? ²)/5
⇒ KEinitial = ½I? ω? ² = (MR²ω? ²)/4
⇒ % loss ⇒ 20%
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