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find the centre of mass of a thin plate of constant density covering the region bounded by the parabola y=25-x^2 and the x axis.

```
6 years ago

```							A thin strip (thickness dx) of the plate, along the vertical line with abscissa x, has mass  y dx = delta*(25 - x^2) dx (The symbol I've seen used for this most often is rho, which looks like a curly slanted p) Hence the mass of the plate is Int[-5 to 5] (25-x^2) dx * delta = [25x - (x^3)/3] [-5 to 5] * delta = 500delta/3 The x coordinate of the centre of mass is Int[-5 to 5] x(25-x^2)dx * delta divided by (500delta/3) = [(25x^2)/2 - (x^4)/4] [-5 to 5] *3/500 = 0 as we would expect. The y coordinate of the centre of mass of each of these strips is, of
course, (25-x^2)/2, and so the y coordinate of the centre of mass of the
plate is  Int[-5 to 5] (((25 - x^2)^2)/2) dx *3/500 = [625x/2 - (25x^3)/3 + (x^5)/10] [-5 to 5] *3/500 = 2*(625*5/2-25*(5^3)/3 + (5^5)/10)*3/500 = 10 Hence the centre of mass is (0, 10)Thanks & Regards,Nirmal SinghAskiitians Faculty
```
6 years ago
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