Question

The second's hand of a watch has $6cm$ length. The speed of tis tip and magnitude of difference in velocity of its at any two perpendicular positions will be respectively:

• A. $2\pi$ and $0$ mm/s
• B. $2\sqrt{2}\pi$ and $4.44$ mm/s
• C. $2\sqrt{2}\pi$ and $2\pi$ mm/s
• D. $2\pi$ and $2\sqrt{3}\pi$ mm/s

Answer 1

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

Second's hand completes a round in 60 sec.

And $R=6cm=60mm$
So,from the relation-

$v=\frac{2\Pi R}{T}=\frac{2\pi 60}{60}=2\pi mm/s$

$v_R=\sqrt{(v_A^2+v_B^2)}$

$v_R=\sqrt{\left(\right(2\pi {)}^2+\left(2\Pi {)}^2\right)}$

$v_R=2\sqrt{2}\pi mm/s$