Thin uniform wire bent - centre of gravity, Mechanical Engineering

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Thin uniform wire bent - centre of gravity:

Find out the C. G. of the thin uniform wire bent into shape ABC as illustrated in Figure.

1683_Thin uniform wire bent.gif

Solution

Assume G be the location of C. G. of the bar as illustrated in Figure

∴ L = L₁+ L₂ = 5 + 5 = 10 m (AB = L₁; BC = L₂)

Taking moments w.r.t. y-axis

L x¯ = L₁ x₁ + L₂ x₂ = 5 × 0 + 5 × 2 = 10

∴ x¯ = 1 m

Taking moments around x axis,

L y¯ = 5 × 2.5 + 5 × 6.5 = 5 × (2.5 + 6.5)

∴ y¯ = 4.5 m

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