JEE Exam > JEE Questions > A frictionless uniform ring of mass m has 2 b...
Start Learning for Free
A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is?
Most Upvoted Answer
A frictionless uniform ring of mass m has 2 beads A and B of mass m ea...
Problem
A frictionless uniform ring of mass m has 2 beads A and B of mass m each; both being able to slide on the ring. Initially, the ring lies on a frictionless horizontal table, and both beads are given velocities v towards the x-axis. The relative velocity of the beads wrt to each other just before they collide is? Explain in detail.
Solution
Let's assume that the ring has a radius R.
Step 1: Find the velocity of the center of mass of the system
The velocity of the center of mass of the system can be found by applying the conservation of momentum.
Initial momentum = Final momentum
2mv = (m + 2m)VCM
VCM = v/3
Step 2: Find the velocity of the beads wrt to the center of mass
Let the velocities of bead A and B wrt to the center of mass be vA and vB respectively.
Using the relative velocity formula, we get:
vrel = vB - vA
Step 3: Find the velocities of the beads
As the ring is a uniform circular motion, the velocity of the beads can be found by using the formula:
v = ωR
where ω is the angular velocity of the ring.
Initial velocity of bead A = v
Velocity of bead A after time t = vA = v - ωt
Initial velocity of bead B = v
Velocity of bead B after time t = vB = v + ωt
Step 4: Find the time taken for the beads to collide
The beads will collide when they meet each other on the ring. Let the time taken for the beads to collide be tc.
Distance traveled by bead A = Distance traveled by bead B
∴ (v - ωtc)tc = (v + ωtc)tc
∴ tc = R/ω
Step 5: Find the relative velocity of the beads just before they collide
Substituting tc in the expression for vrel, we get:
vrel = vB - vA
= (v + ωtc) - (v - ωtc)
= 2ωtc
Community Answer
A frictionless uniform ring of mass m has 2 beads A and B of mass m ea...
Can anyone please solve this for me??
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 frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is?
Question Description
A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is?.
A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is?.
Solutions for A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? 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 frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? defined & explained in the simplest way possible. Besides giving the explanation of
A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is?, a detailed solution for A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? has been provided alongside types of A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? theory, EduRev gives you an
ample number of questions to practice A frictionless uniform ring of mass m has 2 beads A and B of mass m each ;both being able to slide on the ring.initially the ring lies on a frictionless horizontal table and both beads are given velocities v towards +x axis.the relative velocity of the beads wrt to each other just before they collide is? 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