LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
12 views
in Physics by (54.3k points)
closed by
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

1 Answer

0 votes
by (30.0k points)
selected by
 
Best answer
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

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...