Answer:
Explanation:
Center of mass is give as
Xcm = (Σmi•xi) / M
Where i= 1,2,3,4.....
M = m1+m2+m3 +....
x is the position of the mass (x, y)
Now,
Given that,
u1 = (−1, 0, 2) (mass 3 kg),
m1 = 3kg and it position x1 = (-1,0,2)
u2 = (2, 1, −3) (mass 1 kg),
m2 = 1kg and it position x2 = (2,1,-3)
u3 = (0, 4, 3) (mass 2 kg),
m3 = 2kg and it position x3 = (0,4,3)
u4 = (5, 2, 0) (mass 5 kg)
m4 = 5kg and it position x4 = (5,2,0)
Now, applying center of mass formula
Xcm = (Σmi•xi) / M
Xcm = (m1•x1+m2•x2+m3•x3+m4•x4) / (m1+m2+m3+m4)
Xcm = [3(-1, 0, 2) +1(2, 1, -3)+2(0, 4, 3)+ 5(5, 2, 0)]/(3 + 1 + 2 + 5)
Xcm = [(-3, 0, 6)+(2, 1, -3)+(0, 8, 6)+(25, 10, 0)] / 11
Xcm = (-3+2+0+25, 0+1+8+10, 6-3+6+0) / 11
Xcm = (24, 19, 9) / 11
Xcm = (2.2, 1.7, 0.8) m
This is the required center of mass
