First slide

Motion of centre of mass

Question

Three particles of masses 8 kg, 4 kg and 4 kg situated at (4,1), (–2,2) and (1,–3) are acted upon by external forces $\large 6\bar j N,\;-6\bar iN$ and $\large 14\bar iN$ . The acceleration of centre of mass of the system is

Moderate

A

0.625 ms^-2
B

6.25 ms^-2
C

2.2 ms^-2
D

22 ms^-2

Solution

m₁ = 8kg, m₂ = 4kg, m₃ = 4kg
${{\bar F}_1} = 6\hat j,\,\,{{\bar F}_2} = - 6\hat i,\,{\hat {\,F}_3} = 14\hat i$
${{\bar a}_{cm}} = \frac{{{{\bar F}_1} + {{\bar F}_2} + {{\bar F}_3}}}{{{m_1} + {m_2} + {m_3}}} = \frac{{6\widehat j - 6\widehat i + 14\widehat i}}{{16}} = \frac{{8\widehat i + 16\widehat j}}{{16}}$
$a_{cm}=\sqrt \frac {(8)^2+(6)^2}{(16)^2}=\sqrt \frac {100}{256}=\frac {10}{16}=0.625m/s^2$

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