What are the coordinates of the center of mass for the combination of the three

Question

What are the coordinates of the center of mass for the combination of the three objects shown in figure below? The uniform rod has a mass of 9.0 kg, has a length of 32.0 cm, and is located at x 53.0 cm. The oval football has a mass of 2.00 kg, a semimajor axis of 15.0 cm, a semiminor axis of 8.00 cm, and is centered at x--53.0 cm.The spherical volleyball has a mass of 1.00 kg, a radius of 10.0 cm, and is centered at y--32.0 cm. three significant figures.) 30.9 cIm Submit 2) Determine the y coordinate of the center of mass for the combination of the three objects. (Express your answer to three significant figures.) -0.167 cm Submit

Explanation / Answer

m1 = 9 kg m2 = 2 kg m3 = 1 kg

C.G of the rod will be at center of the rod. therefor,

for rod x1 = 53 , y1 = 32/2 = 16;

for ellipse x2 = - 53 , y2 = 0;

for spherical body x3 = 0 , y3 = - 32;

Center of mass

X = (m1x1 +m2x2 + m3x3)/(m1+m2+m3);

= 30.916 cm

Y = (m1y1 +m2y2 + m3y3)/(m1+m2+m3);

= 9.333 cm

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