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  • 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. The magnitude of

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. The magnitude of the acceleration of the CM of the system.

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\begin{array}{l} F_{n r t}=F_{1}+F_{2}+F_{3}=(3 i-2 j+2 k)+(-i+2 j-k)+(i+j+k) \\ \\ \Longrightarrow F_{n d t}=(3 i+j+2 k) N \\ \\ M=1+2+3=6 k g \\ \\ a_{cm}=\frac{F_{n c t}}{M}=\frac{3 i+j+2 k}{6} \\ \\ \Longrightarrow a=\frac{\sqrt{3^{2}+1^{2}+2^{2}}}{6} \\ \\ \Longrightarrow a_{C M}=\frac{\sqrt{14}}{6} m / s^{2} \end{array}

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