Masses 1 kg, 1.5 kg, 2 kg and M kg are situated at (2,1,1), (1,2,1), (2,–2,1) and (–1,4,3). If their centre of mass is situated at (1,1,3/2), the value of M is

m₁ = 1kg, m₂ = 1.5kg, m₃ = 2kg, m₄ = M

x₁ = 2, x₂ = 1, x₃ = 2, x₄ = -1, x_cm = 1

${\mathrm{x}}_{\mathrm{cm}}=\frac{{\mathrm{m}}_1{\mathrm{x}}_1+{\mathrm{m}}_2{\mathrm{x}}_2+{\mathrm{m}}_3{\mathrm{x}}_3+{\mathrm{m}}_4{\mathrm{x}}_4}{{\mathrm{m}}_1+{\mathrm{m}}_2+{\mathrm{m}}_3+{\mathrm{m}}_4}$

$1=\frac{1\left(2\right)+1.5\left(1\right)+2\left(2\right)+\mathrm{M}(-1)}{4.5+\mathrm{M}}$

$\Rightarrow$4.5 + M = 2 + 1.5 + 4 - M 

M = 1.5kg