The relative angular speed of hour hand and second hand of a clock is

The relative angular speed of hour hand and second hand of a clock is
  1. $\frac{359 \pi}{21600}$
  2. $\frac{719 \pi}{21600}$
  3. $\frac{11 \pi}{21600}$
  4. $\frac{9 \pi}{21600}$

Solution

$\frac{\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{\frac{2 \pi}{12 \times 60 \times 60}}{\frac{2 \pi}{60}}=\frac{1}{12 \times 60}$ $\omega_{\mathrm{s}}=720 \omega_{\mathrm{h}}$ $\frac{\omega_{\mathrm{s}}-\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{720-1}{720}$ $\omega_{\mathrm{s}}-\omega_{\mathrm{h}}=\frac{719}{720} \omega_{\mathrm{s}}=\frac{719}{720} \times \frac{2 \pi}{60}=\frac{719 \pi}{21600}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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