GATE ME 2021 Set 2 — Question 62
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Engineering Mechanics → Dynamics → Dynamics of Rigid Bodies
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Question
The wheels and axle system lying on a rough surface is shown in the figure.
Each wheel has diameter and mass . Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is and its mass is . Neglect the moment of inertia of the axle and assume . An effort of is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is __________ (round off to one decimal place).
Correct answer
1.3 to 1.4
Solution
Given:
Mass of each wheel,
Radius of wheel,
Mass of axle,
Radius of axle,
Total mass,
Total moment of inertia (neglecting axle), From the figure, the force is applied at the bottom of the axle. The height of the force from the ground is .Using the principle of rotation about the Instantaneous Center of Rotation (ICR) at the ground contact point:
The linear acceleration of the center is .
Rounding off to one decimal place, we get .
Mass of each wheel,
Radius of wheel,
Mass of axle,
Radius of axle,
Total mass,
Total moment of inertia (neglecting axle), From the figure, the force is applied at the bottom of the axle. The height of the force from the ground is .Using the principle of rotation about the Instantaneous Center of Rotation (ICR) at the ground contact point:
The linear acceleration of the center is .
Rounding off to one decimal place, we get .
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