Test Index

Circular Motion

Section: Physics

Question : 3 of 7

Marks: +1, -0

Solution:

Step 1: Angular velocity of the hour hand

The hour hand of a clock completes one full revolution (

360^{\circ}

2\pi

radians) in

12

hours.

\omega_{\;\text{hour hand }\;}=\;\frac{2\pi}{12\;\text{ hours }\;}=\;\frac{\pi}{6\;\text{ hours }\;}

Step 2: Angular velocity of Earth's rotation

The Earth completes one full rotation (

360^{\circ}

2\pi

radians) in 24 hours.

\omega_{\;\text{Earth }\;}=\;\frac{2\pi}{24\;\text{ hours }\;}=\;\frac{\pi}{12\;\text{ hours }\;}

Step 3: Ratio of angular velocities

\;\;\frac{\omega_{\;\text{hour hand }\;}}{\omega_{\;\text{Earth }\;}}=\;\frac{\;\frac{\pi}{6}}{\frac{\pi}{12}}=\;\frac{12}{6}=2

\;\;\text{ Ratio }\;=2: 1

Correct Option: B)

2: 1

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