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JEE Advanced 2012Paper 1
Exam
JEE Advanced
Year
2012
Paper
Paper 1
Subject
Physics
Chapter
Rotational Motion

JEE Advanced 2012 · Paper 1 · Physics · Rotational Motion

A thin uniform rod, pivoted at O , is rotating in the horizontal...

A thin uniform rod, pivoted at OO, is rotating in the horizontal plane with constant angular speed ω\omega, as shown in the figure. At time t=0t=0, a small insect starts from OO and moves with constant speed vv, with respect to the rod towards the other end. It reaches the end of the rod at t=Tt=T and stops. The angular speed of the system remains ω\omega throughout. The magnitude of the torque (∣τ⃗∣)(|\vec{\tau}|) about OO, as a function of time is best represented by which plot? A thin uniform rod, pivoted at O , is rotating in the horizontal plane with constant angular speed ω , as shown in the

Options

  1. AParagraph: Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS
  2. BParagraph: Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS
  3. CParagraph: Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS
  4. DParagraph: Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS

Correct answer

B. Paragraph: Modern trains are based on Maglev technology in which trains are magnetically leviated, which runs its EDS

Step-by-step solution

Angular momentum, ∣L∣|\mathbf{L}| or L=IωL=I \omega (about axis of rod) Moment of inertia of the rod-insect system. I=Irod +mx2=Irod +mv2t2I=I_{\text{rod }}+m x^{2}=I_{\text{rod }}+m v^{2} t^{2} Here, m=m= mass of insect ∴L=(Irod+mv2t2)ω\therefore \quad L=\left(I_{\mathrm{rod}}+m v^{2} t^{2}\right) \omega Now ∣τ∣=dLdt=(2mv2tω)|\tau|=\frac{d L}{d t}=\left(2 m v^{2} t \omega\right) or ∣τ∣∝t|\tau| \propto t i.e. the graph is straight line passing through origin. After time T,L=T, L= constant ∴∣τ∣ or dLdt=0\therefore \quad|\tau| \text{ or } \frac{d L}{d t}=0 i.e., when the insect stops moving, LL does not change and therefore TT becomes constant.
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