GATE ME 2018 Set 2 — Question 49
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Engineering Mechanics → Dynamics → Dynamics of Rigid Bodies
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Question
A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in m/s) of the centre of the disc is ________ (correct to two decimal places).
Correct answer
6.6 to 6.7
Solution
Let N be the applied force, kg be the mass, and m be the radius. Let be the friction force acting at the contact point.Equations of motion:
Substituting these into the rotation equation:Substitute into the translation equation:The linear acceleration is 6.67 m/s.
1.Translation:
2.Rotation about the center:
For a circular disc, . For rolling without slipping, .Substituting these into the rotation equation:Substitute into the translation equation:The linear acceleration is 6.67 m/s.
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