Three masses m1, m2 and m3 of magnitude 50 kg, 100 kg and 200 kg are connected to a rotating shaft. The corresponding radiuses of rotation are 0.4 m; 0.2 m and 0.1 m respectively and angle between successive masses are 60 and 150. What is the magnitude of balancing mass if its radius of rotation is 0.3 m?a)14.64 kg at angle of 210 from 200 kgb)48.80 kg at angle of 210 from 200 kgc)14.64 kg at angle of 30 from 200 kgd)48.80 kg at angle of 30 from 200 kgCorrect answer is option 'B'. Can you explain this answer?

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GATE Exam > GATE Questions > Three masses m1, m2 and m3 of magnitude 50 kg...

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a)
14.64 kg at angle of 210 from 200 kg
b)
48.80 kg at angle of 210 from 200 kg
c)
14.64 kg at angle of 30 from 200 kg
d)
48.80 kg at angle of 30 from 200 kg

Correct answer is option 'B'. Can you explain this answer?

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Verified Answer

Three masses m1, m2 and m3 of magnitude 50 kg, 100 kg and 200 kg are c...

m₁= 50kg,m₂= 100kg,m₃= 200kg

The horizontal component of centrifugal farce ∑H =

[50 × 0.4 + 100 × 0.2 × cos⁡60^∘ + 200 × 0.1 × cos ⁡210^∘]ω²

= 12.68ω²

The vertical component of centrifugal farce ∑V = [100 × 0.2 × sin⁡60^∘+ 200 × 0.1 × sin ⁡210^∘]ω²= 7.32

ω²

The resultant force,

ω= angular velocity of rotating masses. Suppose the balancing mass M acting moving with angular velocity ω at a radius of rotation 0.3m and it is given as

M × 0.3 × ω²= 14.64ω²

M = 48.8kg

The angle made by resultant with horizontal force anticlockwise, is given as

The location of M = 180^∘+ 30^∘= 210^∘ ta the anticlockwise of 200 kg mass

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Three masses m1, m2 and m3 of magnitude 50 kg, 100 kg and 200 kg are connected to a rotating shaft. The corresponding radiuses of rotation are 0.4 m; 0.2 m and 0.1 m respectively and angle between successive masses are 60 and 150. What is the magnitude of balancing mass if its radius of rotation is 0.3 m?a)14.64 kg at angle of 210 from 200 kgb)48.80 kg at angle of 210 from 200 kgc)14.64 kg at angle of 30 from 200 kgd)48.80 kg at angle of 30 from 200 kgCorrect answer is option 'B'. Can you explain this answer?

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