Okay, so I got the y-coordinate of the center of mass, but I can\'t get the x-co

Question

Okay, so I got the y-coordinate of the center of mass, but I can't get the x-coordinate:

Four very thin rods, each 8.0 m long, are joined to form a square, as part (a) of the drawing shows. The center of mass of the square is located at the coordinate origin. The rod on the right is then removed, as shown in part (b) of the drawing. What are the x- and y-coordinates of the center of mass of the remaining three-rod system?

Xcm = ______m

Ycm = ___0___m

Okay, so I got the y-coordinate of the center of mass, but I can't get the x-coordinate: Four very thin rods, each 8.0 m long, are joined to form a square, as part (a) of the drawing shows. The center of mass of the square is located at the coordinate origin. The rod on the right is then removed, as shown in part (b) of the drawing. What are the x- and y-coordinates of the center of mass of the remaining three-rod system? Xcm = ______m Ycm = ___0___m

Explanation / Answer

Let
    mass of each rod , m = M
    length of each rod , L = 8 m

Case(a): ( with all four rods )
    Total mass, m1 = 4 M
    X-coordinate of center of mass , X1 =0
    Y-coordinate of center of mass , Y1 =0
Case (b) : ( for the removed rod )
    mass, m2 = M
    X-coordinate of center of mass , X2 =L / 2 = 8 /2 = 4.0 m
    Y-coordinate of center of mass , Y2 =0
Center of mass of the remaining part:

    X-coordinate of center of mass , Xcm = (m1 X1 - m2 X2 ) / ( m1- m2 )
                                                               = ( 4 M * 0 - M * 4.0 ) / ( 4 M - M )
                                                               = - 1.33 m
    Y-coordinate of center of mass , Ycm = (m1 Y1 - m2 Y2 ) / ( m1- m2 )
                                                               = ( 4 M * 0 - M * 0 ) / ( 4 M - M )
                                                               = 0 m

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