(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The upper side of a uniform plate of thickness w is given by a function y(x) = 4a+x^2/a. Length of this plate on the x-axis is a . Find x coord of the center of mass of this object, with respect to the origin O . Take density of the plate as p

3. The attempt at a solution

Y(x)= 4a+(x^(2))/a

Can be restated as w.dA=w(4a+(x^(2))/a).dx

therefore using

w.dA.p=dm

w(4a+(x^(2))/a).dx.p=dm

distance from O to CoM qouted as S

will be S= 1/M∫x.dm

S=1/M∫x.w(4a+(x^(2))/a).p.dx

S=1/M.w.p∫(4ax+(x^3)/a).dx

therefore finally , integrating from x=0 to x=a

S=1/M.w.p(2a^3+(a^3)/4)

Mass M can be substituted by = p.w.∫1.dA = p.w.∫y(x).dx from 0 to a

Is this is correct ???!!! :) Thanks in advance

:)

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Center of mass for a function defined body

**Physics Forums | Science Articles, Homework Help, Discussion**