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.
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
∴ L x¯ = ∫ δ L × x = ∫ (a d θ) × (a cos θ)
= 2 a 2
∴ x¯ = 2 a2/ π a = 2 a/ π = 0.637 a