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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 ratio x1x2\frac{x_1}{x_2} is

Options

  1. A2
  2. B12\frac{1}{2}
  3. C2\sqrt{2}
  4. D12\frac{1}{\sqrt{2}}

Correct answer

C. 2\sqrt{2}

Step-by-step solution

12I(2ω)2=12kx1212(2I)(ω)2=12kx22\begin{aligned}\frac{1}{2}I(2 \omega)^2 & =\frac{1}{2}k x_1^2 \\ \frac{1}{2}(2 I)(\omega)^2 & =\frac{1}{2}k x_2^2 \end{aligned} From Eqs. (i) and (ii), we have\frac{x_1}{x_2}=\sqrt{2}\therefore Option (c) is correct.
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