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Question

The length of a seconds hand in watch is $$1$$ $$cm$$. The change in velocity of its tip in $$15\ s$$ is


A
zero
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B
π302 cm/s
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C
π30 cm/s
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D
π230 cm/s
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Solution

The correct option is A $$\displaystyle \dfrac{\pi\sqrt{2} }{30}\ cm/s$$
$$v=\omega r \\ v=1\times \dfrac{2 \pi}{60}\ cm/s = \dfrac{\pi}{30}\ cm/s$$
The magnitude of velocity of tip of the seconds hand remains constant only its direction changes by $$360^0$$ in $$60\ secs$$, i.e., $$90^o$$ in $$15\ secs$$.
Change in velocity  $$\Delta v=v\sqrt { 2 } =\dfrac { \pi \sqrt { 2 }  }{ 30 }\ cm/s$$

Physics

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