Question

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

• A. Zero
• B. $\frac{\pi }{30\sqrt{2}}$ cm /sec
• C. $\frac{\pi }{30}$ cm/sec
• D. $\frac{\pi \sqrt{2}}{30}$ cm /sec

Answer 1

The correct option is D $\frac{\pi \sqrt{2}}{30}$ cm /sec

In 15 second's hand rotate through ${90}^{\circ }$
Change in velocity |$\overline{△}v$| = 2v sin ($\frac{\theta }{2}$)
=2(r$\omega$) sin ($\frac{{90}^{\circ }}{2}$) = 2 $\times$ 1 $\times$ $\frac{2\pi }{T}$ $\times$ $\frac{1}{\sqrt{2}}$
= $\frac{4\pi }{60\sqrt{2}}$ = $\frac{4\pi }{60\sqrt{2}}$ = $\frac{\pi \sqrt{2}cm}{30sec}$ [As T = 60 sec]