GATE ME 2022 Set 2 — Question 39
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Theory of Machines & Vibrations → Balancing, Flywheels & Gyroscopes → Balancing of Rotating Masses
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Question
A rigid body in the - plane consists of two point masses ( kg each) attached to the ends of two massless rods, each of cm length, as shown in the figure. It rotates at RPM counter-clockwise about the -axis passing through point . A point mass of kg, attached to one end of a third massless rod, is used for balancing the body by attaching the free end of the rod to point . The length of the third rod is ________ cm.
Correct answer
(A) 1
Solution
The centrifugal force for a mass at distance rotating with angular velocity is . For static balancing, the net centrifugal force must be zero.Let the two masses be kg and kg at distances cm and cm respectively. The angle between the two rods is .The magnitude of the resultant centrifugal force vector (ignoring as it is common) is:To balance this, a third mass kg must be placed at a distance such that its centrifugal force is equal and opposite to the resultant:Thus, the length of the third rod is 1 cm.
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