find the center of mass of a thin plate of a constant density d, covering the region bounded by the parabola y=5x^2 and the line y=20

Question

anonymous · Answer

centre of mass will certainly lie on the y axis by symmetry we can say that, now to find its y coordinate,
Ycm=integral(y.dm )/integral dm

calculating the numerator,

consider thin strip of width dy at a distance y on the parabola

dm= density * area =D*x*dy
now x=(y/5)^1/2

integral (y.dm) = integ{y*(y/5)^1/2*D*dy }
                                 
                                 D(1/5)^1/2integ{y^3/2.dy  }

                                   D(1/5)^1/2*{ y^5/2}*2/5

now calculating integ dm ={D*x*dy}

                                     =D(1/5)^1/2integ{y^1/2.dy}

                                     =D(1/5)^1/2*  y^3/2 *2/3

now dividing integral (y.dm)  and  integ dm

we get 3/5y

(good question)

anonymous · Answer

did u understand the solution?

anonymous · Answer

still digesting the info...i'm working on my calc 2 final and for whatever reason totally blanked out and am suffering from a brain fart so i'm cramming to get it done in an hour :(

anonymous · Answer

LOL, hmm thats pretty brave, best of luck

anonymous · Answer

thank you

anonymous · Answer

that previous question about finding volume
that is some question,
very good question,
its ppl like you who make OS worth visiting

anonymous · Answer

SERIOUSLY