SATHEE: Rotation 5 Question 5

Rotation 5 Question 5

14. A thin uniform $rod$ , pivoted at $O$ , is rotating in the horizontal plane with constant angular speed $ω$ , as shown in the figure. At time $t = 0$ , a small insect starts from $O$ and moves with constant speed $v$ with respect to the rod towards the other end. It reaches the end of the rod at $t = T$ and stops. The angular speed of the system remains $ω$ throughout.

(2012)

The magnitude of the torque $| τ |$ on the system about $O$ , as a function of time is best represented by which plot? (a)

(c)

(b)

(d)

Show Answer

Answer:

Correct Answer: 14. (b)

Solution:

$| L |$ or $L = I ω$ (about axis of rod)

$I = I_{r o d} + m x^{2} = I_{r o d} + m v^{2} t^{2}$

Here, $m =$ mass of insect

$∴ L = (I_{rod} + m v^{2} t^{2}) ω$

Now $| τ | = \frac{d L}{d t} = (2 m v^{2} t ω)$ or $| τ | \propto t$

i.e. the graph is straight line passing through origin.

After time $T, L =$ constant

$∴ | τ | or \frac{d L}{d t} = 0$

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Rotation 5 Question 5

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