MHT CET · Physics · Motion In Two Dimensions
The ratio of angular speeds of minute hand and hour hand of a watch is
- A \(1: 12\)
- B \(6: 1\)
- C \(12: 1\)
- D \(1: 6\)
Answer & Solution
Correct Answer
(C) \(12: 1\)
Step-by-step Solution
Detailed explanation
\(\omega_{\min }=\frac{2 \pi}{60} \frac{\mathrm{rad}}{\min }\)
and \(\omega_{\mathrm{hr}}=\frac{2 \pi}{12 \times 60} \frac{\mathrm{rad}}{\mathrm{min}}\)
\(\begin{aligned}\therefore \frac{\omega_{\min }}{\omega_{\mathrm{hr}}} &=\frac{2 \pi / 60}{2 \pi / 12 \times 60} \\
&=\frac{12}{1}\end{aligned}\)
and \(\omega_{\mathrm{hr}}=\frac{2 \pi}{12 \times 60} \frac{\mathrm{rad}}{\mathrm{min}}\)
\(\begin{aligned}\therefore \frac{\omega_{\min }}{\omega_{\mathrm{hr}}} &=\frac{2 \pi / 60}{2 \pi / 12 \times 60} \\
&=\frac{12}{1}\end{aligned}\)
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