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JEE Advanced 2007Paper 1
Exam
JEE Advanced
Year
2007
Paper
Paper 1
Subject
Physics
Chapter
Rotational Motion

JEE Advanced 2007 · Paper 1 · Physics · Rotational Motion

Paragraph: P_ 17 - 19 : Paragraph for Questions Nos. 17 to 19 Two...

Paragraph: P17 - 19\mathbf{P}_{17 \text{ - } 19} : Paragraph for Questions Nos. 17 to 19 Two discs AandandBaremountedcoaxiallyonaverticalaxle.ThediscshavemomentsofinertiaIand2I,respectivelyaboutthecommonaxis.DiscAare mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I, respectively about the common axis. Disc A is imparted an initial angular velocity 2ω2 \omega using the entire potential energy of a spring compressed by a distance x1x_1. Disc BB is imparted an angular velocity ω\omega by a spring having the same spring constant and compressed by a distance x2x_2. Both the discs rotate in the clockwise direction.Question: The loss of kinetic energy during the above process is

Options

  1. AIω22\frac{I \omega^2}{2}
  2. Biω23\frac{i \omega^2}{3}
  3. CIω24\frac{I \omega^2}{4}
  4. DIω26\frac{I \omega^2}{6}

Correct answer

B. iω23\frac{i \omega^2}{3}

Step-by-step solution

Loss of kinetic energy =Ki−Kf=K_i-K_f ={12I(2ω)2+12(2I)(ω)2}−12(3I)(43ω)2=13Iω2\begin{aligned}& =\left\{\frac{1}{2}I(2 \omega)^2+\frac{1}{2}(2 I)(\omega)^2\right\}-\frac{1}{2}(3 I)\left(\frac{4}{3} \omega\right)^2 \\ & =\frac{1}{3}I \omega^2 \end{aligned}\therefore Option (b) is correct.
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