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The relative angular speed of hour hand and second hand of a clock is
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The correct answer is:
$\frac{719 \pi}{21600}$
$\frac{\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{\frac{2 \pi}{12 \times 60 \times 60}}{\frac{2 \pi}{60}}=\frac{1}{12 \times 60}$
$\omega_{\mathrm{s}}=720 \omega_{\mathrm{h}}$
$\frac{\omega_{\mathrm{s}}-\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{720-1}{720}$
$\omega_{\mathrm{s}}-\omega_{\mathrm{h}}=\frac{719}{720} \omega_{\mathrm{s}}=\frac{719}{720} \times \frac{2 \pi}{60}=\frac{719 \pi}{21600}$
$\omega_{\mathrm{s}}=720 \omega_{\mathrm{h}}$
$\frac{\omega_{\mathrm{s}}-\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{720-1}{720}$
$\omega_{\mathrm{s}}-\omega_{\mathrm{h}}=\frac{719}{720} \omega_{\mathrm{s}}=\frac{719}{720} \times \frac{2 \pi}{60}=\frac{719 \pi}{21600}$
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