The relative angular speed of hour hand and second hand of a clock is (in rad/s)

The correct option is (C).
Concept: The angular speed is given by \(\omega=\frac{\Delta \theta}{\Delta t}\)
Relative angular speed is given by, \(\omega=\omega_{\mathrm{s}}-\omega_{\mathrm{h}}\)
The angular speed of the second dial is \(\omega_{\mathrm{s}}=\frac{2 \pi}{60}=\frac{\pi}{30} \mathrm{rad} / \mathrm{s}\)
The angular speed of the hour dial is
\(\omega_{\mathrm{h}}=\frac{2 \pi}{3600 \times 12}=\frac{\pi}{21600} \mathrm{rad} / \mathrm{s}\)
Therefore, relative angular speed is given by,
\(\omega=\omega_{\mathrm{s}}-\omega_{\mathrm{h}}=\frac{\pi}{30}-\frac{\pi}{21600}=\frac{719}{21600} \mathrm{rad} / \mathrm{s}\)