oubaas
dcm = (m1*d1+m2*(d1+d2)+m3(d1+d2+d3)) /(m1+m2+m3)
dcm = (21*1.5+15*(1.5+2.5)+52*(1.5+2.5+3.6))/(21+15+52) = 5.53 cm
?
(a) x = [m₁d₁ + m₂*(d₁+d₂) + m₃*(d₁+d₂+d₃)] / (m₁+m₂+m₃)
(b) x = [21*1.5 + 15*4.0 + 52*7.6]g·cm / (21+15+52)g
x = 5.53 cm (I'd round to 5.5 cm)
(c) x' = [m₁*-d₂ + m₃*d₃] / (m₁+m₂+m₃)
(d) x' = [21*-2.5 + 52*3.6]g·cm / 88g = 1.53 cm ≈ 1.5 cm
Of course it is, since the middle bead is 4 cm from the left end of the rod (and 1.5cm + 4.0 cm = 5.5 cm)