Find the Center of Mass of a Lamina in the Shape

question 11

Multiple Choice

Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length $a = 15$ if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse. Assume the vertex opposite the hypotenuse is located at $( 0,0 )$ , and that the sides are along the positive axes.

• A) \(( 6,6 )\)
• B) \(( 6,15 )\)
• C) \(( 5,6 )\)
• D) \(( 15,15 )\)
• E) None of these

---

Definitions:

Equation

A statement that asserts the equality of two expressions, usually represented by the symbol "=".

Slope-Intercept Form

A way of writing the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Slope

The measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Point

A specific location in space defined by coordinates in a given dimension.