JEE Exam > JEE Questions > A disc of radius 1 m is rotating about centra...
Start Learning for Free
A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?
Verified Answer
A disc of radius 1 m is rotating about central axis with angular veloc...
v = rw
here v =velocity
r=radius
w= angular velocity
for center radius will be 0
hence velocity also be 0
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
A disc of radius 1 m is rotating about central axis with angular veloc...
Given:
- Radius of the disc, r = 1 m
- Angular velocity, ω = 2 rad/s
- Velocity of point P, vP = 4j m/s
To find:
Velocity of the center of the disc
Explanation:
The velocity of any point on a rotating disc can be divided into two components:
1. Tangential velocity: This component is in the direction of the tangent to the point's path on the disc.
2. Radial velocity: This component is in the direction perpendicular to the tangent and points towards the center of the disc.
Since point P is moving with a velocity of 4j m/s, it means that only the tangential velocity component is present.
Let's denote the tangential velocity component as vT.
Deriving the formula:
The tangential velocity of a point on a rotating disc can be calculated using the formula:
vT = rω
where r is the distance of the point from the axis of rotation and ω is the angular velocity.
In this case, r = 1 m and ω = 2 rad/s, so the tangential velocity vT is:
vT = 1 * 2 = 2 m/s
Calculating the velocity of the center of the disc:
The velocity of the center of the disc can be found by adding the tangential velocity of point P to the radial velocity of point P.
Since the point P is on the circumference of the disc, its radial velocity component is equal to the tangential velocity component, but in the opposite direction. Let's denote the radial velocity component as vR.
Therefore, vR = -2j m/s
The velocity of the center of the disc is the vector sum of the tangential velocity and the radial velocity:
vCenter = vT + vR
Substituting the values, we get:
vCenter = 2i + (-2j)
vCenter = 2i - 2j
Answer:
The velocity of the center of the disc is (2i - 2j) m/s. Therefore, the correct option is (4) (2i - 4j) m/s.
- Radius of the disc, r = 1 m
- Angular velocity, ω = 2 rad/s
- Velocity of point P, vP = 4j m/s
To find:
Velocity of the center of the disc
Explanation:
The velocity of any point on a rotating disc can be divided into two components:
1. Tangential velocity: This component is in the direction of the tangent to the point's path on the disc.
2. Radial velocity: This component is in the direction perpendicular to the tangent and points towards the center of the disc.
Since point P is moving with a velocity of 4j m/s, it means that only the tangential velocity component is present.
Let's denote the tangential velocity component as vT.
Deriving the formula:
The tangential velocity of a point on a rotating disc can be calculated using the formula:
vT = rω
where r is the distance of the point from the axis of rotation and ω is the angular velocity.
In this case, r = 1 m and ω = 2 rad/s, so the tangential velocity vT is:
vT = 1 * 2 = 2 m/s
Calculating the velocity of the center of the disc:
The velocity of the center of the disc can be found by adding the tangential velocity of point P to the radial velocity of point P.
Since the point P is on the circumference of the disc, its radial velocity component is equal to the tangential velocity component, but in the opposite direction. Let's denote the radial velocity component as vR.
Therefore, vR = -2j m/s
The velocity of the center of the disc is the vector sum of the tangential velocity and the radial velocity:
vCenter = vT + vR
Substituting the values, we get:
vCenter = 2i + (-2j)
vCenter = 2i - 2j
Answer:
The velocity of the center of the disc is (2i - 2j) m/s. Therefore, the correct option is (4) (2i - 4j) m/s.
Community Answer
A disc of radius 1 m is rotating about central axis with angular veloc...
0
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?
Question Description
A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?.
A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?.
Solutions for A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? defined & explained in the simplest way possible. Besides giving the explanation of
A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s?, a detailed solution for A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? has been provided alongside types of A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? theory, EduRev gives you an
ample number of questions to practice A disc of radius 1 m is rotating about central axis with angular velocity 2 rad/s. If a point P Lying on its circumference as shown is moving with velocity 4j m/s, then velocity of centre of disc is (1) (2i 4j) m/s (2) (4i 2i) m/s (3) (-2i 4j) m/s (4) (2i-4j) m/s? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup