Question

Three particles of masses 1 kg, 2 kg, and 3 kg are subjected to forces (3i-2j+2k)N,(-i+2j-k)N and (i+j+k)N respectively. Find the magnitude of the acceleration of the CM of the system.

Answer 1

$F_{net}=F_1+F_2+F_3=(3i-2j+2k)+(-i+2j-k)+(i+j+k)$

$⟹F_{net}=(3i+j+2k)N$

$M=1+2+3=6kg$

$\overrightarrow{a_{CM}}=\frac{F_{net}}{M}=\frac{3i+j+2k}{6}$

$⟹a=\frac{\sqrt{3^2+1^2+2^2}}{6}$

$⟹a_{CM}=\frac{\sqrt{14}}{6}m/s^2$