GATE ME 2016 Set 3 — Question 41
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Engineering Mechanics → Dynamics → Work-Energy Formulation
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Question
A circular disc of radius mm and mass kg, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed of the disc when it reaches position B is _________ m/s.
Acceleration due to gravity m/s.
Correct answer
19.9 to 20.1
Solution
Using the principle of conservation of energy for a body rolling without slipping:
Total Energy at A = Total Energy at B
For a circular disc, the moment of inertia . For rolling without slipping, , so .
Substituting these into the energy equation:
Given m and m/s:
m/s.
Total Energy at A = Total Energy at B
For a circular disc, the moment of inertia . For rolling without slipping, , so .
Substituting these into the energy equation:
Given m and m/s:
m/s.
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