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Physics · MOTION IN A PLANE

हिन्दी

An insect trapped in a circular groove of radius \( 12\text{ cm} \) moves along the groove steadily and completes \( 7 \) revolutions in \( 100\text{ s} \). What are the angular speed \( \omega \) and the linear speed \( v \) of the insect? (Use \( \pi = 3.14 \))

  1. \( \omega = 0.22\text{ rad/s} \), \( v = 2.6\text{ cm/s} \)
  2. \( \omega = 0.88\text{ rad/s} \), \( v = 10.6\text{ cm/s} \)
  3. \( \omega = 0.44\text{ rad/s} \), \( v = 5.3\text{ cm/s} \)
  4. \( \omega = 0.44\text{ rad/s} \), \( v = 2.3\text{ cm/s} \)

Correct answer · Option 3

\( \omega = 0.44\text{ rad/s} \), \( v = 5.3\text{ cm/s} \)

Explanation

Frequency \( \nu = 7/100\text{ s}^{-1} \). Angular speed \( \omega = 2\pi\nu = 2 \times 3.14 \times 0.07 = 0.44\text{ rad/s} \). Linear speed \( v = \omega R = 0.44 \times 12 = 5.3\text{ cm/s} \).
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