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  4. Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side l . The X coordinate of center of mass is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-pp5dbmsd8rmz.png />

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Q. Three masses $2 \, kg, \, 3 \, kg$ and $4 \, kg$ are lying at the corners of an equilateral triangle of side $l$ . The $X$ coordinate of center of mass is

Question

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

The $\left(X\right)$ coordinate of center of mass is,
$X_{c m}=\frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3}}{m_{1} + m_{2} + m_{3}}$
$X_{c m}=\frac{2 \left(0\right) + 3 l + 4 \left(\frac{l}{2}\right)}{2 + 3 + 4}$
$X_{c m}=\frac{5}{9}l$