
A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at any point on a circular path?
a. \[20\,m/s\]
b. \[\sqrt 2\,m/s\]
c. \[10\,m/s\]
d. \[2\,m/s\]
Answer
163.2k+ views
Hint:When a body is moving in a circular path then the position of the body along the circular path changes with time. As we know, the rate of change in the linear position of the body with respect to time is called linear velocity. The rate of change of the angular position with respect to time is called the angular velocity.
Formula used:
\[v = \omega r\]
where v is the linear velocity, \[\omega \] is the angular velocity and r is the distance of the point from the axis of rotation.
Complete step by step solution:
It is given that the body is whirled in a horizontal circle. The radius of the circle is given as 20 cm. The angular velocity of the body is given as 10 rad/s. We need to find the linear velocity at any point on a circular path.

Image: Body motion in a circular path
Let the linear velocity of the body is v. The distance of the body from the axis of rotation, i.e. from the center of the circular path is equal to the radius of the circular path.
\[r = 20\,cm = 0.2\,m\]
\[\Rightarrow \omega = 10\,rad/s\]
When a body is moving in a given circular path then the position of the body along the circular path changes with time.The rate of change in the linear position of the body with respect to time is called the linear velocity, v.
The linear velocity of the body is linearly related to the angular velocity of the body in the circular path as,
\[v = \omega r\]
Putting the values, we get the linear velocity of the body in circular orbit as,
\[v = 10 \times 0.2\,m/s\]
\[\therefore v = 2\,m/s\]
Hence, the linear velocity of the body is equal to 2 m/s.
Therefore, the correct option is d.
Note: We should be careful while using the relation between the linear velocity and the angular velocity as it is for the instantaneous velocity. So, if we find the linear velocity of the accelerated body in a circular path then the obtained linear velocity will be corresponding to the angular velocity at that instant in time.
Formula used:
\[v = \omega r\]
where v is the linear velocity, \[\omega \] is the angular velocity and r is the distance of the point from the axis of rotation.
Complete step by step solution:
It is given that the body is whirled in a horizontal circle. The radius of the circle is given as 20 cm. The angular velocity of the body is given as 10 rad/s. We need to find the linear velocity at any point on a circular path.

Image: Body motion in a circular path
Let the linear velocity of the body is v. The distance of the body from the axis of rotation, i.e. from the center of the circular path is equal to the radius of the circular path.
\[r = 20\,cm = 0.2\,m\]
\[\Rightarrow \omega = 10\,rad/s\]
When a body is moving in a given circular path then the position of the body along the circular path changes with time.The rate of change in the linear position of the body with respect to time is called the linear velocity, v.
The linear velocity of the body is linearly related to the angular velocity of the body in the circular path as,
\[v = \omega r\]
Putting the values, we get the linear velocity of the body in circular orbit as,
\[v = 10 \times 0.2\,m/s\]
\[\therefore v = 2\,m/s\]
Hence, the linear velocity of the body is equal to 2 m/s.
Therefore, the correct option is d.
Note: We should be careful while using the relation between the linear velocity and the angular velocity as it is for the instantaneous velocity. So, if we find the linear velocity of the accelerated body in a circular path then the obtained linear velocity will be corresponding to the angular velocity at that instant in time.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Degree of Dissociation and Its Formula With Solved Example for JEE

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
