Mathematics, 04.04.2020 10:54 pineapplefun
The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − x2 together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is inversely proportional to its distance from the origin.
Answers: 1
whose radious are 1 and 4 respectively.
, let density at any point is 
and distance from the origin is r be such that,
where k is a constant.
where A is the total region and D is curves.
. in polar coordinate 
![=3k\big[-\cos\theta\big]_{0}^{\pi}](/tpl/images/0582/1695/fa2fb.png)
![=3k\big[-\cos\pi+\cos 0\big]](/tpl/images/0582/1695/e6a2a.png)
. in polar coordinate 
![=3k\big[\sin\theta\big]_{0}^{\pi}](/tpl/images/0582/1695/749f9.png)
![=3k\big[\sin\pi-\sin 0\big]](/tpl/images/0582/1695/aa42e.png)
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The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − x2 together with the po...
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