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Lesson Worksheet: Center of Gravity of Laminas Mathematics

In this worksheet, we will practice finding the position of the center of gravity of a lamina composed of standard shapes in 2D.


Where does the center of gravity of a uniform triangular lamina lie?

  • AAt the intersection of its diagonals
  • BAt the intersection of its altitudes
  • CAt the intersection of its medians


Where does the center of gravity of a uniform circular disk lie?

  • AOn the circumference
  • BAt the center of the circle
  • CAt the center of the radius


A uniform lamina is bounded by the parallelogram 𝐴𝐡𝐢𝐷. Where does its center of gravity lie?

  • AAt point 𝐴
  • BAt point 𝐡
  • CAt the intersection point of the parallelogram’s diagonals


In the figure shown, find the position of the center of mass of the uniform triangular lamina 𝐴𝐡𝐢, considering 𝐴 to be the origin point.

  • Aο€Ό2π‘Ž,5π‘Ž2
  • Bο€Ό8π‘Ž3,10π‘Ž3
  • Cο€Ό4π‘Ž3,5π‘Ž3
  • Dο€Ό4π‘Ž3,10π‘Ž3
  • Eο€Ό8π‘Ž3,5π‘Ž3


A uniform rectangular lamina has a length of 63 cm and a width of 59 cm. It is divided into three equal-sized rectangles along its length; the last of these rectangles has been folded over so that it lies flat on the middle rectangle as shown in the figure. Find the coordinates of the center of gravity of the lamina in this form.

  • Aο€Ό492,592
  • Bο€Ό14,593
  • Cο€Ό593,14
  • Dο€Ό592,492


The diagram shows a uniform plane figure. Given that the grid is composed of unit squares, find the coordinates of the figure’s center of mass.

  • Aο€Ό42πœ‹+1436πœ‹+30,83
  • Bο€Ό42πœ‹+1516πœ‹+30,3
  • Cο€Ό42πœ‹+1436πœ‹+30,3
  • Dο€Ό42πœ‹+1436πœ‹+30,4
  • Eο€Ό42πœ‹+1516πœ‹+30,83


A uniform square lamina 𝐴𝐡𝐢𝐷 has a side length 𝑙. Another uniform lamina 𝐡𝐢𝐸 of the same density, shaped as an isosceles triangle, is attached to the square such that 𝐸 lies outside the square and 𝐡𝐸=𝐢𝐸. Given that the square’s side length is 53 times the length of the triangle’s height, find the center of mass of the system.

  • Aο€Ό4365𝑙,12π‘™οˆ
  • Bο€Ό2865𝑙,12π‘™οˆ
  • Cο€Ό2039𝑙,13π‘™οˆ
  • Dο€Ό4665𝑙,13π‘™οˆ


A uniform lamina in the form of a square 𝐴𝐡𝐢𝐷 of side length 28 cm has a mass of 54 grams. Masses of 10, 8, 4, and 8 grams are fixed at 𝐴, 𝐡, 𝐢, and 𝐷 respectively. Find coordinates of the center of mass of the system.

  • Aο€Ό25919,27319
  • B(13,13)
  • C(22,13)
  • Dο€Ό13,623


A uniform lamina in the form of an equilateral triangle of side length 24 cm has a mass of 298 g. A mass of 149 g is attached to the lamina at one of the trisection points of 𝐴𝐡 as shown in the figure. Determine the coordinates of the system’s center of gravity.

  • Aο€Ώ323,8√33
  • Bο€Ώ12,16√33
  • Cο€Ώ323,16√33
  • Dο€»12,4√3


Find, to the nearest degree, the angle that the line π‘ˆπ‘‡ makes with the vertical if the given uniform lamina is hung freely from 𝑄.

This lesson includes 62 additional questions and 414 additional question variations for subscribers.

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