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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.

**Q1: **

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

**Q2: **

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

**Q3: **

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

- AAt point
- BAt point
- CAt the intersection point of the parallelogramβs diagonals

**Q4: **

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

- A
- B
- C
- D
- E

**Q5: **

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.

- A
- B
- C
- D

**Q6: **

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

- A
- B
- C
- D
- E

**Q7: **

A uniform square lamina has a side length . Another uniform lamina of the same density, shaped as an isosceles triangle, is attached to the square such that lies outside the square and . Given that the squareβs side length is times the length of the triangleβs height, find the center of mass of the system.

- A
- B
- C
- D

**Q8: **

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

- A
- B
- C
- D

**Q9: **

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 as shown in the figure. Determine the coordinates of the systemβs center of gravity.

- A
- B
- C
- D

**Q10: **

Find, to the nearest degree, the angle that the line makes with the vertical if the given uniform lamina is hung freely from .