Need help to solve a Physics problem on length and density

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Description

A rod of length 30.0 cm has linear density (mass per length) given by λ = 50.0 + 20.0x where x is the distance from one end, measured in meters, and λ is in grams / meter. (a) What is the mass of the rod? (b) How far from the x = 0 end is its center of mass?

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Explanation & Answer

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The length of the rod is L=30.0 cm

The linear density (mass per length) is given by the formula λ =m/L

1.  Given λ = 50.0 + 20.0x, where x is the distance from one end in meters, for x= L=30.0 cm=0.30m, the mass of the rod is m=λ*L

m=(50.0 + 20.0*0.30)*0.30

m=16.8g

1.  The center of mass of the rod is in:


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