Question

4. Two students were asked to find the center of mass of a thin plate of constant density 8 covering the region bounded above by y=1 - 22 and below by y=-2. The center of mass of a typical vertical strip is represented by (,y) (see figure). Both students agree that the mass differential dm = 8 dA = density-length - width should be dm = 8.00 - 22] - [-2]). dr. (a) Student 1 claims that (1, Ý) is (7, (la – 2) – 1–2]). Student 2 claims that (č,) is (2, 15-7*=='). Which student is correct and why? (b) The x-coordinate of the center of mass is 1. Calculate the y-coordinate of the center of mass.

Answer 1

Since density is constant all over. We dont need to consider this in calculating center of mass. See the below solution-

(a) Student 2 is correct who claims that while (7,5)= (x, Ena) because f(n)+ g(n) is the mid point of stoop f(n)-g(n) represents tength of the strip. density is constant y coordinate is found out wing- 92 - S [(f(n) - Calw I don Sfem-gemilan (6) b whene A = a a, b aul intersection points which are n-n=-n 2²-22=0 & n(n-2)=0 9 2=0,2 2 2 S(2n-r) du 6 (x-n-(-n) du [2]. - } 3 - 2 ugon 3 TIM o 2 (67+*+- 21? **) 8.

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2. د - 3 =9 3 8 0 3 8 X = 3x - 8 ک = 3 S

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