A uniform disc of mass 5 kg and radius 2 m is rotating with 10 rad/s. Now another identical disc is gently placed on first disc. Because of friction, both disc acquire common angular velocity. Loss of kinetic energy in process is _______ J.

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alok kumar singh | Contributor-Level 10

4 weeks ago

COAM gives Iw₀ = 2Iw

$ω = \frac{ω_{0}}{2}$

Loss in KE = $\frac{1}{2} I ω_{0}^{2} - \frac{1}{2} (2 I) {(\frac{ω_{0}}{2})}^{2}$

$= \frac{1}{2} I ω_{0}^{2}$

$= \frac{1}{4} \times 5 \times \frac{2}{2} \times 100 = 250 J$

COAM gives Iw0 = 2Iw <math> <mrow> <mi>ω</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> Loss in KE =  <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>I</mi> <msubsup> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> <mo>−</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mrow> <mo> (</mo> <mrow> <mn>2</mn> <mi>I</mi> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1820403011"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>I</mi> <msubsup> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>0</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msubsup> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1820403012"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mo>×</mo> <mn>5</mn> <mo>×</mo> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <mn>0</mn> <mn>0</mn> <mo>=</mo> <mn>2</mn> <mn>5</mn> <mn>0</mn> <mtext> </mtext> <mi>J</mi> </mrow> </math>

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A uniform disc of mass 5 kg and radius 2 m is rotating with 10 rad/s. Now another identical disc is gently placed on first disc. Because of friction, both disc acquire common angular velocity. Loss of kinetic energy in process is _______ J.

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