Finding the Center of Mass of a Group of Two or More Particles

 AP Physics 2 Skills Practice

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  • 1.

    In the following image a group of particles is shown. Find the center of mass.

    Answers:

    • {eq}(\frac{2}{33},\frac{-38}{33}) {/eq}

    • {eq}(\frac{-8}{32},\frac{5}{22}) {/eq}

    • {eq}(\frac{8}{32},\frac{-5}{22}) {/eq}

    • {eq}(\frac{-2}{33},\frac{38}{33}) {/eq}

  • 2.

    In the following graph a group of particles is shown calculate the center of mass.

    Answers:

    • {eq}(\frac{-23}{59},\frac{-30}{59}) {/eq}

    • {eq}(\frac{23}{59},\frac{-30}{59}) {/eq}

    • {eq}(\frac{-3}{59},\frac{30}{59}) {/eq}

    • {eq}(\frac{3}{59},\frac{30}{59}) {/eq}

  • 3.

    Calculate the center of mass of the group of particles shown in the next graph.

    Answers:

    • {eq}(\frac{35}{49},\frac{-5}{49}) {/eq}

    • {eq}(\frac{-35}{49},\frac{5}{49}) {/eq}

    • {eq}(\frac{-44}{49},\frac{5}{49}) {/eq}

    • {eq}(\frac{44}{49},\frac{-5}{49}) {/eq}

  • 4.

    A group of particles is shown in the figure below. Determine the center of mass.

    Answers:

    • {eq}(\frac{-21}{53},\frac{26}{53}) {/eq}

    • {eq}(\frac{-18}{53},\frac{33}{53}) {/eq}

    • {eq}(\frac{18}{53},\frac{-33}{53}) {/eq}

    • {eq}(\frac{21}{53},\frac{26}{53}) {/eq}

  • 5.

    In the graph we can observe a set of particles. The center of mass must be calculated.

    Answers:

    • {eq}(\frac{120}{87},\frac{-35}{57}) {/eq}

    • {eq}(\frac{-120}{87},\frac{35}{57}) {/eq}

    • {eq}(\frac{-130}{57},\frac{35}{57}) {/eq}

    • {eq}(\frac{130}{57},\frac{-35}{57}) {/eq}

  • 6.

    Calculate the center of mass in the group of particles that we can observe in the image below.

    Answers:

    • {eq}(-5,\frac{142}{41}) {/eq}

    • {eq}(5,\frac{-142}{41}) {/eq}

    • {eq}(3,\frac{-104}{41}) {/eq}

    • {eq}(-3,\frac{104}{41}) {/eq}

  • 7.

    We must find the center of mass of the group of particles shown in the graph.

    Answers:

    • {eq}(\frac{4}{120},3) {/eq}

    • {eq}(\frac{3}{44},2) {/eq}

    • {eq}(\frac{-4}{120},-3) {/eq}

    • {eq}(\frac{-3}{44},-2) {/eq}

  • 8.

    What is the center of mass of the particles found in this graph?

    Answers:

    • {eq}(\frac{-1}{2},\frac{-1}{6}) {/eq}

    • {eq}(\frac{1}{2},\frac{1}{6}) {/eq}

    • {eq}(\frac{-3}{2},\frac{-27}{100}) {/eq}

    • {eq}(\frac{3}{2},\frac{27}{100}) {/eq}

  • 9.

    In the following image a group of particles is shown. What is the center of mass?

    Answers:

    • {eq}(\frac{-27}{14},\frac{111}{35}) {/eq}

    • {eq}(\frac{-17}{14},\frac{101}{35}) {/eq}

    • {eq}(\frac{17}{14},\frac{-101}{35}) {/eq}

    • {eq}(\frac{27}{14},\frac{-111}{35}) {/eq}

  • 10.

    Calculate the center of mass of the group of particles shown in the next graph.

    Answers:

    • {eq}(\frac{79}{100},\frac{47}{100}) {/eq}

    • {eq}(\frac{-79}{100},\frac{-47}{100}) {/eq}

    • {eq}(\frac{47}{100},\frac{79}{100}) {/eq}

    • {eq}(\frac{-47}{100},\frac{-79}{100}) {/eq}

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  • 11.

    In the graph we can observe a set of particles. The center of mass must be calculated.

    Answers:

    • {eq}(\frac{-1}{3},\frac{-2}{3}) {/eq}

    • {eq}(\frac{1}{3},\frac{2}{3}) {/eq}

    • {eq}(\frac{33}{100},\frac{29}{12}) {/eq}

    • {eq}(\frac{-33}{100},\frac{29}{12}) {/eq}

  • 12.

    We must find the center of mass of the group of particles shown in the graph.

    Answers:

    • {eq}(\frac{39}{17},\frac{12}{17}) {/eq}

    • {eq}(\frac{49}{17},\frac{9}{17}) {/eq}

    • {eq}(\frac{-49}{17},\frac{-9}{17}) {/eq}

    • {eq}(\frac{-39}{17},\frac{-12}{17}) {/eq}

  • 13.

    In the following image a group of particles is shown. Find the center of mass.

    Answers:

    • {eq}(\frac{28}{13},\frac{27}{13}) {/eq}

    • {eq}(\frac{18}{13},\frac{17}{13}) {/eq}

    • {eq}(\frac{27}{13},\frac{28}{13}) {/eq}

    • {eq}(\frac{17}{13},\frac{18}{13}) {/eq}

  • 14.

    In the following image a group of particles is shown. What is the center of mass?

    Answers:

    • {eq}(\frac{-23}{8},\frac{3}{8}) {/eq}

    • {eq}(\frac{-23}{8},\frac{-3}{8}) {/eq}

    • {eq}(\frac{-13}{8},\frac{-21}{24}) {/eq}

    • {eq}(\frac{-13}{8},\frac{21}{24}) {/eq}

  • 15.

    In the following graph a group of particles is shown. Calculate the center of mass.

    Answers:

    • {eq}(\frac{-53}{39},\frac{-35}{39}) {/eq}

    • {eq}(\frac{-23}{39},\frac{-25}{39}) {/eq}

    • {eq}(\frac{23}{39},\frac{-25}{39}) {/eq}

    • {eq}(\frac{53}{39},\frac{-35}{39}) {/eq}

  • 16.

    Calculate the center of mass of the group of particles shown in the following image.

    Answers:

    • {eq}(\frac{-36}{33},\frac{-57}{33}) {/eq}

    • {eq}(\frac{-58}{53},\frac{-87}{53}) {/eq}

    • {eq}(\frac{-58}{53},\frac{87}{53}) {/eq}

    • {eq}(\frac{-36}{33},\frac{57}{33}) {/eq}

  • 17.

    Determine the center of mass of the group of particles shown in the following image.

    Answers:

    • {eq}(\frac{5}{6},3) {/eq}

    • {eq}(\frac{-1}{6},2) {/eq}

    • {eq}(\frac{1}{6},2) {/eq}

    • {eq}(\frac{-5}{6},3) {/eq}

  • 18.

    Find the center of mass of the group of particles shown in the image.

    Answers:

    • {eq}(\frac{83}{101},\frac{59}{101}) {/eq}

    • {eq}(\frac{-83}{101},\frac{59}{101}) {/eq}

    • {eq}(\frac{-183}{101},\frac{159}{101}) {/eq}

    • {eq}(\frac{183}{101},\frac{159}{101}) {/eq}

  • 19.

    In the following image, calculate the center of mass of the group of particles shown.

    Answers:

    • {eq}(\frac{14}{5},\frac{2}{5}) {/eq}

    • {eq}(\frac{-14}{5},\frac{2}{5}) {/eq}

    • {eq}(\frac{14}{5},\frac{-2}{5}) {/eq}

    • {eq}(\frac{-14}{5},\frac{-2}{5}) {/eq}

  • 20.

    In this image, the center of mass of the group of particles shown must be calculated.

    Answers:

    • {eq}(\frac{-9}{35},\frac{4}{7}) {/eq}

    • {eq}(\frac{9}{35},\frac{-4}{7}) {/eq}

    • {eq}(\frac{-9}{35},\frac{-4}{7}) {/eq}

    • {eq}(\frac{9}{35},\frac{4}{7}) {/eq}

  • 21.

    In the group of particles shown in this image, the center of mass must be determined.

    Answers:

    • {eq}(\frac{48}{37},\frac{-77}{37}) {/eq}

    • {eq}(\frac{-48}{37},\frac{77}{37}) {/eq}

    • {eq}(\frac{-48}{37},\frac{-77}{37}) {/eq}

    • {eq}(\frac{48}{37},\frac{77}{37}) {/eq}

  • 22.

    The following image represents a group of particles in which the center of mass must be found.

    Answers:

    • {eq}(\frac{-5}{7},\frac{-11}{21}) {/eq}

    • {eq}(\frac{-5}{7},\frac{11}{21}) {/eq}

    • {eq}(\frac{5}{7},\frac{-11}{21}) {/eq}

    • {eq}(\frac{5}{7},\frac{11}{21}) {/eq}

  • 23.

    The table below shows a group of particles in which the center of mass is to be calculated.

    Answers:

    • {eq}(\frac{-3}{10},\frac{11}{10}) {/eq}

    • {eq}(\frac{-3}{10},\frac{-11}{10}) {/eq}

    • {eq}(\frac{3}{10},\frac{-11}{10}) {/eq}

    • {eq}(\frac{3}{10},\frac{11}{10}) {/eq}

  • 24.

    Calculate the center of mass of the group of particles shown in the following image.

    Answers:

    • {eq}(\frac{7}{19},-3) {/eq}

    • {eq}(\frac{-7}{19},-3) {/eq}

    • {eq}(\frac{7}{19},3) {/eq}

    • {eq}(\frac{-7}{19},3) {/eq}

  • 25.

    In the following image, calculate the center of mass of the group of particles shown.

    Answers:

    • {eq}(\frac{-77}{72},\frac{125}{72}) {/eq}

    • {eq}(\frac{77}{72},\frac{125}{72}) {/eq}

    • {eq}(\frac{77}{72},\frac{-125}{72}) {/eq}

    • {eq}(\frac{-77}{72},\frac{-125}{72}) {/eq}

  • 26.

    The following image represents a group of particles in which the center of mass must be found.

    Answers:

    • {eq}(\frac{44}{23},\frac{29}{23}) {/eq}

    • {eq}(\frac{44}{23},\frac{-29}{23}) {/eq}

    • {eq}(\frac{-44}{23},\frac{-29}{23}) {/eq}

    • {eq}(\frac{-44}{23},\frac{29}{23}) {/eq}

  • 27.

    Determine the center of mass of the group of particles shown in the following image.

    Answers:

    • {eq}(\frac{-40}{21},\frac{-19}{21}) {/eq}

    • {eq}(\frac{19}{21},\frac{-37}{21}) {/eq}

    • {eq}(\frac{40}{21},\frac{19}{21}) {/eq}

    • {eq}(\frac{40}{21},\frac{-19}{21}) {/eq}

  • 28.

    In this image, the center of mass of the group of particles shown must be calculated.

    Answers:

    • {eq}(\frac{-20}{67},\frac{66}{67}) {/eq}

    • {eq}(\frac{-20}{67},\frac{-66}{67}) {/eq}

    • {eq}(\frac{20}{67},\frac{66}{67}) {/eq}

    • {eq}(\frac{20}{67},\frac{-66}{67}) {/eq}

  • 29.

    Calculate the center of mass of the group of particles shown in the following image.

    Answers:

    • {eq}(\frac{-1}{47},\frac{-45}{47}) {/eq}

    • {eq}(\frac{1}{47},\frac{-45}{47}) {/eq}

    • {eq}(\frac{-1}{47},\frac{45}{47}) {/eq}

    • {eq}(\frac{1}{47},\frac{45}{47}) {/eq}

  • 30.

    Determine the center of mass of the group of particles shown in the following image.

    Answers:

    • {eq}(\frac{126}{64},-5) {/eq}

    • {eq}(\frac{126}{64},-3) {/eq}

    • {eq}(\frac{121}{63},-5) {/eq}

    • {eq}(\frac{121}{63},-3) {/eq}

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