Question

three particles of masses 3g, 5g and 8g are situated at point (2,2,2), (-3,1,4), and (-1,3,-2) respectively. Determine the position vector of their center of mass.​

Answer 1

Given info : Three particles of masses 3g, 5g and 8g are situated at point (2,2,2), (-3,1,4), and (-1,3,-2) respectively

To find : The position vector of their centre of mass is...

solution : we know, centre of mass the system of masses is given by, $\left(\frac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3},\frac{m_1y_1+m_2y_2+m_3y_3}{m_1+m_2+m_3},\frac{m_1z_1+m_2y_2+m_3y_3}{m_1+m_2+m_3}\right)$

here, m₁ = 3g , m₂ = 5g and m₃ = 8g

(x₁ , y₁ , z₁) = (2, 2, 2)

(x₂ , y₂ , z₂) = (-3, 1, 4)

(x₃ , y₃ , z₃) = (-1, 3, -2)

so centre of mass = [(3 × 2 + 5 × -3 + 8 × -1)/(3 + 5 + 8) , (3 × 2 + 5 × 1 + 8 × 3)/(3 + 5 + 8), (3 × 2 + 5 × 4 + 8 × -2)/(3 + 5 + 8)]

= [(6 - 15 - 8)/16 , (6 + 5 + 24)/16 , (6 + 20 - 16)/16 ]

= [-17/16 , 35/16 , 5/8 ]

Therefore the centre of mass of the masses is (-17/16, 35/16 , 5/8)

Answer 2

Answer:

thank you for watching the answer. and don't forget to make me as a Brainlist