Question

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

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

Answer 1

Answer: (D)

$\frac{\pi \sqrt{2}}{30}cm/s$

$v=\omega rv=1\times \frac{2\pi }{60}cm/s=\frac{\pi }{30}cm/s$

The magnitude of velocity of tip of the seconds hand remains constant only its direction changes by ${360}^0$ in $60secs$, i.e., ${90}^o$ in $15secs$.
Change in velocity $\Delta v=v\sqrt{2}=\frac{\pi \sqrt{2}}{30}cm/s$