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Find the moment about the x axis of a wire of constant velocity...?
Find the moment about the x -axis of a wire of constant density (density=c) that lies along the curve y=x^(1/2) from x=0 to x=1 . Hint: Your answer should have a c in it!
1 Answer
- Elizabeth MLv 78 years agoFavorite Answer
An element of arc
ds=√(1+(dy/dx)^2)dx
=√[1+ 1/(4x)]dx= √[(4x+1)/(4x)]dx
The moment about the x-axis is cyds
= cx^(1/2)√[(4x+1)/(4x)]dx
=(1/2)c√(4x+1) dx
And integrating gives [(1/12)c(4x+1)^(3/2)] from x=0 to x=1
giving (1/12)c{5^(3/2) - 1}