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An ant is trapped inside a circular groove of a radius 10 cm. If it moves steadily along the boundary of the groove and completes 5 revolutions in 100 s. Then what is the linear velocity of the ant?
1. 3.14 cm/s
2. 0.44 cm/s
3. 2.75 cm/s
4. 1.94 cm/s

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Correct Answer - Option 1 : 3.14 cm/s

The correct answer is option 1) i.e. 3.14 cm/s


  • Angular velocity is the velocity associated with objects moving in a curved path.
    • While on a curved path, the displacement is the change in angle about the point of rotation or curved motion.
    • Angular velocity, \(ω =\frac{angle}{time} =\frac{dθ}{dt}\)
    • The tangent to any point on the curved path gives the direction of the linear velocity of the object at that point.
  • The angular velocity ω is related to the linear velocity of an object v by the equation

⇒ v = rω 

Where r is the radius of the curvature.

  • The angular velocity is also given by ω = 2πf 

Where f is the frequency.

  • Frequency is the number of repetition of an event per unit time. It is given by

\(⇒ f = \frac{1}{T}\)

Where T is the time taken.


Given that:

Radius, r = 10 cm

  • Frequency, 

\(⇒ f = \frac{1}{T} = \frac{5}{100} = 0.05 \:Hz\)

  • Angular velocity, 

⇒ ω = 2πf = 2π × 0.05 = 0.314 rad/s

  • Linear velocity,

 v = rω = 10 × 0.314 = 3.14 cm/s

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