GATE ME 2019 Set 2 — Question 48
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Theory of Machines & Vibrations → Balancing, Flywheels & Gyroscopes → Balancing of Rotating Masses
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Question
Two masses and having mass and , respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through perpendicular to the plane of the figure. The radii of rotation of the masses and are and , respectively. The angle between lines and is . If , , and , then the balance mass to be placed at a radius of is ______ kg (round off to two decimal places).
Correct answer
41 to 42
Solution
For static balancing of a rotating system, the vector sum of the centrifugal forces must be zero. Since all masses are in the same plane, we can use the products:Let be along the -axis and be along the -axis (since the angle is ).
The resultant product is:To balance this, a mass must be placed at radius such that:Rounding to two decimal places, the balance mass is .
The resultant product is:To balance this, a mass must be placed at radius such that:Rounding to two decimal places, the balance mass is .
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