Question

If the length of the seconds hand in a stop-clock is $ 3\,cm $ , the angular velocity and linear velocity of the tip is:

• A. $ 0.2047\text{ }rad/s,\text{ }0.0314\text{ }m{{s}^{-1}} $
• B. $ 0.2547\text{ }rad/s,\text{ }0.314\text{ }m{{s}^{-1}} $
• C. $ 0.1472\text{ }rad/s,\text{ }0.06314\text{ }m{{s}^{-1}} $
• D. $ 0.1047\text{ }rad/s,\text{ }0.00314\text{ }m{{s}^{-1}} $
• E. $ 0.347\text{ }rad/s,\text{ }0.314\text{ }m{{s}^{-1}} $

Answer 1

Answer: (D)

Angular velocity of seconds hand $ =\frac{2\pi }{60} $
$ =\frac{\pi }{30} $
$ =\frac{3.14}{30} $
$ =0.1047\text{ }rad/s
$ Linear velocity, $ v=r\omega $
$ =3\times {{10}^{-2}}\times 0.1047 $
$ =0.00314\,m/s $