Include a drawing 1. Assume that the bracket shown is made from a homogeneous (uniform) flat plate of negligible thickness. Each of the four holes has diameter \( d \), which is **given**. What are the \( x \) and \( z \) coordinates of the bracket’s mass center? (The angle \( \theta \) in the figure is irrelevant.) [Hint: Because the diameter of the holes is given, you must account for them.]### Diagram DescriptionThe diagram illustrates a bracket made from a flat plate bent at a right angle. It features two surfaces—one vertical and one horizontal—with each surface having two holes. The holes are uniformly distributed, and the diameter of each hole is labeled \( d \).- **Vertical Plate:** - The holes are aligned vertically. - The top and bottom holes are \( 5d \) apart. - The distance from the top of the vertical plate to the top hole is \( 2d \). - The distance from the bottom of the vertical plate to the bottom hole is \( 2d \).- **Horizontal Plate:** - The distance from the bend to the vertical alignment of the holes is \( 4d \). - The distance from the edge of the horizontal plate to the holes horizontally is \( 2d \).- **Overall Bracket Layout:** - The entire structure forms an L-shape. - Both the vertical and horizontal plates have identical hole spacing horizontally (\( 2d \)) from their respective nearest edges. - A \( z \)-axis is shown as perpendicular to the bent edge, and an \( x \)- and \( y \)-axis are outlined on the horizontal plane. The angle \( \theta \) is irrelevant for this problem. The problem involves calculating the center of mass in the \( x \) (horizontal) and \( z \) (vertical) directions, considering that the material is uniform and the holes reduce the mass in those specific regions.

each segment with respective centroid is tabulated as below............... SEGMENT A(mm2) x(mm) z (mm) xA (mm3) ZA (mm3) 1 120 x 80 =9600 0 0.5 x 60 0 384000 2 120 x 60=7200 0.5 x 60 =30 0 216000 0 3 -2 x (11 x 52) = -157.0796 0 80-20=60 0 -9424.776 4 -2 x (11 x 52)=-157.0796 0 20 0 -3141.592 5 =21600 =371433.6 centroid about x axis is expressed as x=∑x¯A∑Ax¯= 216000 mm3/16485.84mm2x¯=13.1mmcentroid about x-axis is expressed as ∑xa∑A⇒371433.632 mm3/16485.84mm2=22.73 mm