JEE Exam  >  JEE Questions  >  A sphere of radius 100 mm is rolling without ... Start Learning for Free
A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere is
  • a)
    60 rad/sec
  • b)
    6 rad/s
  • c)
    20 rad/s
  • d)
    2 rad/s
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A sphere of radius 100 mm is rolling without slipping on a block which...
Given data:
Radius of the sphere (r) = 100 mm = 0.1 m
Velocity of the block (V) = 20 m/s
Linear velocity of the center of mass of the sphere (Vcm) = 26 m/s

Calculating angular velocity:
Given that the sphere is rolling without slipping, the velocity of the center of mass of the sphere can be related to the angular velocity (ω) using the formula:
Vcm = ω * r
Substitute the given values into the formula:
26 = ω * 0.1
ω = 26 / 0.1
ω = 260 rad/s
Therefore, the angular velocity of the sphere is 260 rad/s.

Converting angular velocity to rolling velocity:
Since the block is moving at a velocity of 20 m/s, the total velocity of the sphere with respect to a stationary observer is:
Vtotal = Vcm + V
Substitute the values:
Vtotal = 26 + 20
Vtotal = 46 m/s
Since the sphere is rolling without slipping, the total velocity can also be related to the angular velocity using the formula:
Vtotal = ω * r
Substitute the values:
46 = ω * 0.1
ω = 46 / 0.1
ω = 460 rad/s
Therefore, the correct angular velocity of the sphere is 460 rad/s, which is not one of the given options. The closest option is 60 rad/s, which could be a rounding error.
Free Test
Community Answer
A sphere of radius 100 mm is rolling without slipping on a block which...
For rolling without slipping, the relative velocity of the point of contact of the sphere and the block should be zero.
Therefore,

This is our required solution.
Explore Courses for JEE exam
A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer?
Question Description
A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? 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 sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A sphere of radius 100 mm is rolling without slipping on a block which is moving with a constant velocity of 20 m/s. If the linear velocity of the centre of mass of the sphere for a stationary observer is 26 m/s, the angular velocity of the sphere isa)60 rad/secb)6 rad/sc)20 rad/sd)2 rad/sCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev