Question

The seconds hand of a watch has length $6\text{cm}$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

• A. $2\pi$ and $0\text{mm/s}$
• B. $2\sqrt{2}\pi$ and $4.44\text{mm/s}$
• C. $2\sqrt{2}\pi$ and $2\pi \text{mm/s}$
• D. $2\pi$ and $2\sqrt{2}\pi \text{mm/s}$

Answer 1

The correct option is D $2\pi$ and $2\sqrt{2}\pi \text{mm/s}$

Consider the perpendicular positions shown in the figure.


Speed of the seconds hand
$v=\frac{2\pi r}{\text{time in one revolution}}$
$\Rightarrow v=\frac{2\pi \times 6}{60}=2\pi \text{mm/s}$

Magnitude of difference in velocities $=|\overrightarrow{v_f}-\left(\overrightarrow{-v_i}\right)|$
$=\sqrt{v^2+v^2}=\sqrt{8{\pi }^2}=2\sqrt{2}\pi \text{mm/s}$