Worksheet: Center of Mass

In this worksheet, we will practice finding an object's center of mass and analyzing the effect of the position of the center of mass on an object's stability.

Q1:

The object shown in the diagram has a uniform density. Which of the points ๐ด, ๐ต, ๐ถ, and ๐ท is closest to the center of mass of the object?

  • APoint ๐ท
  • BPoint ๐ถ
  • CPoint ๐ต
  • DPoint ๐ด

Q2:

Which of the following statements most correctly defines the center of mass of an object?

  • AAn objectโ€™s center of mass is the point at the center of the object.
  • BAn objectโ€™s center of mass is the point in the object nearest to the ground.
  • CAn objectโ€™s center of mass is the point in the object that has the greatest density.
  • DAn objectโ€™s center of mass is the point from which the objectโ€™s weight acts.

Q3:

The skewed object shown in the diagram can be supported by one of the objects ๐ด, ๐ต, ๐ถ, and D. Which of these objects would most stably support the skewed object? ๐ด, ๐ต, ๐ถ, and ๐ท all have the same masses as each other and all produce the same amount of friction at their points of contact as each other. All the objects have the same uniform density.

  • A ๐ต
  • B ๐ด
  • C ๐ท
  • D ๐ถ

Q4:

An object has uniform density. The object is shown in the diagram at rest on a horizontal surface, rotated to stand on different sides.

Which of the orientations A, B, C, D, and E has the greatest horizontal distance between the objectโ€™s center of mass and the nearest point to the left of the center of mass at which no reaction force from the surface can act on the object?

  • AOrientation E
  • BOrientation D
  • COrientation A
  • DOrientation B
  • EOrientation C

Which of the orientations A, B, C, D, and E has the least horizontal distance between the objectโ€™s center of mass and the nearest point to the left of the center of mass at which no reaction force from the surface can act on the object?

  • AOrientation A
  • BOrientation C
  • COrientation D
  • DOrientation B
  • EOrientation E

In which of the orientations A, B, C, D, and E would a leftward horizontal force applied to the top of the object, as shown in the diagram, most easily result in the object tipping over and coming to rest in a different orientation? Assume that the friction between the shape and the surface is the same for all orientations.

  • AOrientation E
  • BOrientation C
  • COrientation D
  • DOrientation A
  • EOrientation B

Q5:

The object shown in the diagram consists of two parts. Each part has a uniform density, but the density of the smaller part is twice that of the larger part. Which of the points ๐ด, ๐ต, ๐ถ, and ๐ท is closest to the center of mass of the object?

  • APoint ๐ด
  • BPoint ๐ท
  • CPoint ๐ถ
  • DPoint ๐ต

Q6:

Which of the points ๐ด, ๐ต, ๐ถ, and ๐ท is the closest to the center of mass of the object shown? The object has uniform density.

  • APoint ๐ถ
  • BPoint ๐ด
  • CPoint ๐ต
  • DPoint ๐ท

Q7:

A hollow cylinder with thick walls rests on its outer wall, as shown in the diagram. The diagram includes a cross-sectional view of the cylinder, on which the labeled points , , , and are shown. Which of the points is on a horizontal line that passes through the cylinderโ€™s center of mass?

  • A
  • B
  • C
  • D

Q8:

The diagram shows a drinking glass under three different conditions. The glass is shown empty, and its center of mass is shown at its geometric center. Water is then added to the glass, and the center of mass of the partially filled glass is shown; this is the center of the combined mass of the glass and the water. Finally, an ice cube is placed in the water, and a pencil is used to push the ice cube into the water so that it is at rest, with its topmost face just at the height of the water level. Which of the points ๐ด, ๐ต, ๐ถ, and ๐ท most correctly shows the position of the center of the combined mass of the glass, water, and ice?

  • A ๐ถ
  • B ๐ท
  • C ๐ต
  • D ๐ด

Q9:

The objects shown in the diagram both have the same mass as each other, and both have uniform densities. Which of the lines ๐ด, ๐ต, ๐ถ, and ๐ท intersects the combined center of mass of both objects?

  • ALine ๐ถ
  • BLine ๐ท
  • CLine ๐ด
  • DLine ๐ต

Q10:

Which of the points ๐ด, ๐ต, ๐ถ, and ๐ท most correctly shows the position of the center of mass of the spring in the diagram? The coils of the spring all have the same uniform density as each other.

  • A ๐ท
  • B ๐ด
  • C ๐ต
  • D ๐ถ

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