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Need clarity, kindly explain! If each mass in the figure is 1 kg, what is the x location of the center of mass?

If each mass in the figure is 1 kg, what is the x location of the center of mass?

  • Option 1)

    0.50  

  • Option 2)

    0.67

  • Option 3)

    1.00

  • Option 4)

    1.33

 
Answers (1)
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As we discussed in

Centre of Mass of a system of N discrete particles -

x_{cm}=\frac{m_{1}x_{1}+m_{2}x_{2}.........}{m_{1}+m_{2}.......}

y_{cm}=\frac{m_{1}y_{1}+m_{2}y_{2}+m_{3}y_{3}.........}{m_{1}+m_{2}+m_{3}.......}

z_{cm}=\frac{m_{1}z_{1}+m_{2}z_{2}+m_{3}z_{3}.........}{m_{1}+m_{2}+m_{3}.......}

- wherein

m1, m2 ........... are mass of each  particle  x1, x2 ..........y1, y2 ............ z1, z2 are respectively x, y, & z coordinates of particles.

 

 x_c=\frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}=\frac{0\times 1+1\times 1+1\times 2}{1+1+1}

x_c=\frac{3}{3}=1


Option 1)

0.50  

Incorrect

Option 2)

0.67

Incorrect

Option 3)

1.00

Correct

Option 4)

1.33

Incorrect

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