Question 1

Which of the following best describes the center of mass (CM) of an object?

Accepted Answer

The average position of all the mass in an object, weighted by mass.

Question 2

For a uniform rectangular solid, where is the center of mass located?

Accepted Answer

At the geometric center of the solid.

Question 3

Given three rectangles with areas $$A_1$$, $$A_2$$, and $$A_3$$ and their respective centers at $$(x_1$, y_1$)$$, $$(x_2$, y_2$)$$, and $$(x_3$, y_3$)$$, what is the formula for the $$x-$$coordinate of the center of mass of the composite shape?

Accepted Answer

$$x_{CM} = \frac{A_1$ x_1$ + A_2$ x_2$ + A_3$ x_3$}{A_1$ + A_2$ + A_3$}$$

Question 4

Why is the concept of center of mass important for high jumpers, as shown in the provided image?

Accepted Answer

It enables them to pass their center of mass under the bar while their body clears it.

Question 5

Suppose you have a slab of uniform material. If the mass of each piece is proportional to its surface area, how can you compute the center of mass?

Accepted Answer

By averaging the positions of each piece weighted by their surface areas.

Question 6

Which statement is true about the center of gravity (CG) and center of mass (CM) for most practical purposes in architecture?

Accepted Answer

They can be used interchangeably for most calculations.

Question 7

An object is suspended from different points and allowed to hang freely. The intersection of the vertical lines from each suspension point determines:

Accepted Answer

The center of gravity of the object.

Question 8

For a two-dimensional uniform object, mass is proportional to:

Accepted Answer

Area

Question 9

If the net force on a rigid body is zero, which of the following statements is true?

Accepted Answer

The center of mass must remain still.

Question 10

Which formula correctly expresses the $$y-$$coordinate of the center of mass for $$n$$ discrete masses $$m_i$$ located at positions $$y_i$$?

Accepted Answer

$$y_{CM} = \frac{\sum_{i=1}^{n} m_i y_i}{\sum_{i=1}^{n} m_i}$$

Question 11

A composite object is made of two uniform bars, each with their own center of mass on the same line. What can be said about the center of mass of the whole object?

Accepted Answer

It must lie somewhere on the line joining the two centers of mass.

Question 12

Why is it important to support an object at its center of mass?

Accepted Answer

To ensure the object does not rotate and remains stable.

Question 13

Which of the following is a correct method to experimentally determine the center of gravity of an irregularly shaped object?

Accepted Answer

Balance the object at several points and find the intersection of the vertical lines from each support.

Question 14

If an object rotates and vibrates, which point will move linearly as if all the forces were concentrated at it?

Accepted Answer

The center of mass.

Question 15

In the context of rotational dynamics, what is the 'point of application'?

Accepted Answer

The specific location at which each individual force acts on the body.

Question 16

A steel plate is cut into three rectangles with areas 6 cm², 3 cm², and 5 cm². Their centers are at (1,1), (3,3), and (6,2) respectively. What is the $$x-$$coordinate of the center of mass?

Accepted Answer

$$x_{CM} = \frac{6 	imes 1 + 3 	imes 3 + 5 	imes 6}{6 + 3 + 5}$$

Question 17

Which of the following is NOT a correct statement about the center of mass?

Accepted Answer

It is always located at the lowest point of the object.

Question 18

If a rigid body is acted upon by equal and opposite forces at different points, what motion will result?

Accepted Answer

The body will rotate about its center of mass.

Question 19

Which of the following best explains why the center of mass formula uses a weighted average?

Accepted Answer

Because the contribution of each part to the center of mass depends on its mass.

M06Center of Mass and Center of Gravity: Principles and Applications in Physics

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