show that the centre of a rod of mass M and length L lies midway between the ends assuming that the rod has uniform cross section per unit length

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Physics

Young

15 February, 14:57

show that the centre of a rod of mass M and length L lies midway between the ends assuming that the rod has uniform cross section per unit length

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Raven · Answer 1

The cross section per unit length is uniform, so ρ is constant.

The center of mass is therefore:

x_avg = (∫₀ᴸ x ρ dL) / (∫₀ᴸ ρ dL)

x_avg = (∫₀ᴸ x dL) / (∫₀ᴸ dL)

x_avg = (½ L²) / (L)

x_avg = ½ L