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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​

User Mike
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1 Answer

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Step-by-step explanation:

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

User Anchit Mittal
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