# 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

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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

CONCEPT:

• 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.

CALCULATION:

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