MHT CET · Physics · Rotational Motion
The relative angular speed of hour hand and second hand of a clock is
- A \(\frac{359 \pi}{21600}\)
- B \(\frac{719 \pi}{21600}\)
- C \(\frac{11 \pi}{21600}\)
- D \(\frac{9 \pi}{21600}\)
Answer & Solution
Correct Answer
(B) \(\frac{719 \pi}{21600}\)
Step-by-step Solution
Detailed explanation
\(\frac{\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{\frac{2 \pi}{12 \times 60 \times 60}}{\frac{2 \pi}{60}}=\frac{1}{12 \times 60}\)
\(\omega_{\mathrm{s}}=720 \omega_{\mathrm{h}}\)
\(\frac{\omega_{\mathrm{s}}-\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{720-1}{720}\)
\(\omega_{\mathrm{s}}-\omega_{\mathrm{h}}=\frac{719}{720} \omega_{\mathrm{s}}=\frac{719}{720} \times \frac{2 \pi}{60}=\frac{719 \pi}{21600}\)
\(\omega_{\mathrm{s}}=720 \omega_{\mathrm{h}}\)
\(\frac{\omega_{\mathrm{s}}-\omega_{\mathrm{h}}}{\omega_{\mathrm{s}}}=\frac{720-1}{720}\)
\(\omega_{\mathrm{s}}-\omega_{\mathrm{h}}=\frac{719}{720} \omega_{\mathrm{s}}=\frac{719}{720} \times \frac{2 \pi}{60}=\frac{719 \pi}{21600}\)
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