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IIT JEE Advanced 2012 Paper 1

Section: Physics

Question : 4 of 60

Marks: +1, -0

Solution:

We have τ =

\frac{dL}{dt}

, where L is the angular momentum. Now,

τ =

\frac{d}{dt} (I_{\text{sys}} \omega)

\omega \left( \frac{dI_{\text{sys}}}{dt} \right)

\omega \frac{d}{dt} (I_{\text{rod}} + m r^2)

where r is the instantaneous distance of the insect from O.

Therefore,

τ =

m \omega 2 r \left( \frac{dr]}{dt} \right)

= 2mrωv = 2mvω(vt) =

2 m v^2 \omega t

⇒ τ α t

Since the insect stops at the other end, v = 0 and τ = 0. Therefore, the resultant plot is a simple straight line.

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