KCET · Physics · Semiconductors
The ratio of angular speed of a second-hand to the hour-hand of a watch is
- A \( 720: 1 \)
- B 60:1
- C ( \( 3600: 1 \)
- D 72: \( 1 \)
Answer & Solution
Correct Answer
(A) \( 720: 1 \)
Step-by-step Solution
Detailed explanation
For second-hand, \(t=60 \mathrm{~s}\)
So, angular speed \(\omega=\frac{2 \pi}{60}\)
For hour-hand, \(\mathrm{t}=12\) hour \(=12 \times 60 \times 60 \mathrm{~s}\)
So, angular speed, \(\omega^{\prime}=\frac{2 \pi}{12 \times 60 \times 60}\)
Then ratio
\(\frac{\omega}{\omega^{\prime}}=\frac{\frac{2 \pi}{60}}{\frac{2 \Pi}{12 \times 60 \times 60}}=12 \times 60=720\)
Therefore, ratio of angular speed of a second-hand to the hour-hand of a watch is \(720: 1\)
So, angular speed \(\omega=\frac{2 \pi}{60}\)
For hour-hand, \(\mathrm{t}=12\) hour \(=12 \times 60 \times 60 \mathrm{~s}\)
So, angular speed, \(\omega^{\prime}=\frac{2 \pi}{12 \times 60 \times 60}\)
Then ratio
\(\frac{\omega}{\omega^{\prime}}=\frac{\frac{2 \pi}{60}}{\frac{2 \Pi}{12 \times 60 \times 60}}=12 \times 60=720\)
Therefore, ratio of angular speed of a second-hand to the hour-hand of a watch is \(720: 1\)
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