GATE ME 2016 Set 3 — Question 46
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Theory of Machines & Vibrations → Balancing, Flywheels & Gyroscopes → Balancing of Rotating Masses
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Question
Two masses are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses is attached to the opposite sides of the shaft in the vertical plane as shown in figure. 
Consider and . For the system to be dynamically balanced, should be ________ kg.
Correct answer
1.9 to 2.1
Solution
For a system to be dynamically balanced, the net centrifugal force and the net moment of centrifugal forces about any point must be zero.
Thus, the value of for dynamic balancing is 2 kg.
1.Static Balance: . Since the masses are on opposite sides, the forces cancel out if and . This condition is satisfied by the symmetry of the arrangement.
2.Dynamic Balance: . Let's take the moment about the position of the left mass (origin ):
- Left mass at , eccentricity (downwards).
- Left mass at , eccentricity (upwards).
- Right mass at , eccentricity (downwards).
- Right mass at , eccentricity (upwards).
Thus, the value of for dynamic balancing is 2 kg.
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