Four particle of masses m, 2m, 3m and 4m are | vedclass

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Question

Therefore the coordinates of centre of mass are.

$x_{\alpha n}=\frac{m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3}+m_{4} x_{4}}{m_{1}+m_{2}+m_{3}+m_{4}}=\fra

Vedclass · Accepted Answer

$\left( {\,0.95a,\,\,\frac{{\sqrt 3 }}{4}a\,} \right)$

Vedclass · Answer

Therefore the coordinates of centre of mass are.

$x_{\alpha n}=\frac{m_{1} x_{1}+m_{2} x_{2}+m_{3} x_{3}+m_{4} x_{4}}{m_{1}+m_{2}+m_{3}+m_{4}}=\frac{M(o)+2 M\left(\frac{a}{2}\right)+3 M\left(\frac{3 a}{2}\right)+a M(a)}{M+2 M+3 M+4 M}$

$\Rightarrow x_{c m}=\frac{\frac{M a}{2}+\frac{9 M A}{2}+\frac{8 M a}{2}}{10 M}=\frac{9 M a}{10 M}$

$\Rightarrow x_{c m}=\frac{9 a}{10}$

$y_{c n}=\frac{m_{1} y_{1}+m_{2} y_{2}+m_{3} y_{3}+m_{4} y_{4}}{m_{1}+m_{2}+m_{3}+m_{4}}=\frac{M(0)+2 M\left(\frac{\sqrt{3} a}{2}\right)+3 M\left(\frac{\sqrt{3} a}{2}\right)+4 M(0)}{M+2 M+3 M+4 M}$

$y_{c m}=\frac{\frac{5 \sqrt{3 M a}}{2}}{10 M}=\frac{5 \sqrt{3} M a}{20 M}$

$\Rightarrow y_{c m}=\frac{\sqrt{3 a}}{4}$

Therefore, the coordinates of the centre of mass are.

$\left(x_{c m} \cdot y_{c m}\right)=\left(\frac{9 a}{10}, \frac{\sqrt{3} a}{4}\right)$

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