Find out the centre of gravity of a wire, Mechanical Engineering

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Find out the centre of gravity of a wire:

Find out the C. G. of a wire of uniform cross-section bent into shape of a semicircle as illustrated in Figure.

2204_Thin uniform wire bent.gif

Solution

Refer to Figure illustrating length of wire ACB = π a, where a = radius of semicircle with center at O.

For an element (δL) of this wire that = a d θ

2454_Find out the centre of gravity of a wire.png

∴ L x¯ = ∫ δ L × x = ∫ (a d θ) × (a cos θ)

1113_Find out the centre of gravity of a wire1.png

= 2 a ²

∴ x¯ = 2 a²/ π a = 2 a/ π = 0.637 a

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