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 $|\overline{\Delta v}|=2vsin\left(\frac{\theta }{2}\right)$

$=2\left(r\omega \right)sin\left(\frac{{90}^{\circ }}{2}\right)=2\times 1\times \frac{2\pi }{T}\times \frac{1}{\sqrt{2}}$
$=\frac{4\pi }{60\sqrt{2}}=\frac{\pi \sqrt{2}cm}{30sec}[AsT=60sec]$