Question

The length of hour hand of a wrist watch is $1.5cm$. Find magnitude of Linear velocity ?

• A. $3.18\times {10}^{-6}$
• B. $2.18\times {10}^{-6}$
• C. $1.18\times {10}^{-6}$
• D. $4.18\times {10}^{-6}$

Answer 1

The correct option is B $2.18\times {10}^{-6}$

Length of hour hand of a wrist watch is $1.5$cm

We know that angular velocity,$\omega =\frac{2\pi }{T}$

where $T$ is the time taken to complete one circle by hour hand.

$\omega =\frac{2\pi }{T}=\frac{2\pi }{12\times 60\times 60}$rad/s$=\frac{\pi }{12\times 1800}$

We know that $v=\omega r$

where $v$ is the linear velocity, $\omega$ is the angular velocity and $r$ is the radius of the hour hand.

So,$v=\frac{\pi }{12\times 1800}\times 1.5$

$=\frac{\pi }{12\times 1200}$

$=\frac{\pi }{14400}$

$=\frac{22}{7\times 14400}$

$=2.18\times {10}^{-6}$m/s