Q126 / 180 · KCET 2015 · Physics

The ratio of angular speed of a second-hand to the hour-hand of a watch is

  • Correct answer
    A
    \( 720: 1 \)
  • B
    60:1
  • C
    ( \( 3600: 1 \)
  • D
    72: \( 1 \)

Solution

For second-hand, $t=60 \mathrm{~s}$ So, angular speed $\omega=\frac{2 \pi}{60}$ For hour-hand, $\mathrm{t}=12$ hour $=12 \times 60 \times 60 \mathrm{~s}$ So, angular speed, $\omega^{\prime}=\frac{2 \pi}{12 \times 60 \times 60}$ Then ratio $\frac{\omega}{\omega^{\prime}}=\frac{\frac{2 \pi}{60}}{\frac{2 \Pi}{12 \times 60 \times 60}}=12 \times 60=720$ Therefore, ratio of angular speed of a second-hand to the hour-hand of a watch is $720: 1$

Hence, the correct answer is option: 'A'.

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