GATE ME 2017 Set 1 — Question 41
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Engineering Mechanics → Dynamics → Work-Energy Formulation
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Question
Two disks A and B with identical mass () and radius () are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mass concentrated at the rim, while Disk B has its mass uniformly distributed. At the bottom of the plane, the ratio of velocity of the center of disk A to the velocity of the center of disk B is
Correct answer
(A) √((3)/(4))
Solution
For a body of mass and radius rolling down an inclined plane of height without slipping, the conservation of energy gives:Since the disk rolls without slipping, . Substituting this:Solving for velocity :For Disk A: Mass is concentrated at the rim, so it behaves like a thin ring. Its moment of inertia is .For Disk B: Mass is uniformly distributed, so it is a solid disk. Its moment of inertia is .Ratio:Thus, the correct option is (A).
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