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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.
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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.
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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?
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