Question

The velocity of the tip of the second hand of a watch is $10\text{cm/s}$. The change in velocity of its tip in $15\text{s}$ is

• A. zero
• B. $\frac{20}{\sqrt{2}}\text{cm/s}$
• C. $\frac{10}{\sqrt{2}}\text{cm/s}$
• D. $10\text{cm/s}$

Answer 1

The correct option is B $\frac{20}{\sqrt{2}}\text{cm/s}$

The formula for change in velocity of tip is given by:
$\Delta v=2v\sin \frac{\theta }{2}$

Here, $\theta ={90}^{\circ }$ as the second hand rotates for $15s$
$\Delta v=2v\sin \frac{90}{2}=2\times 10\times \frac{1}{\sqrt{2}}$
$\Delta v=\frac{20}{\sqrt{2}}\text{cm/s}$