Seven particles, each of mass m are placed at the seven corners of a cube of side 'a' but one corner is vacant, as shown in figure. The co-ordinates of the centre of mass of the system is :-

Question

\\ (A) $(\frac{2 a}{7}, \frac{2 a}{7}, \frac{2 a}{7})$ \\ (B) $(\frac{3 a}{7}, \frac{3 a}{7}, \frac{3 a}{7})$ \\ (C) $(\frac{a}{3}, \frac{a}{3}, \frac{a}{3})$ \\ (D) $(\frac{5 a}{11}, \frac{5 a}{11}, \frac{5 a}{11})$

TestHub · Accepted Answer

With all 8 corners filled, the centre of mass is at the cube centre $(\frac{a}{2}, \frac{a}{2}, \frac{a}{2})$ . Remove the particle at the vacant corner (a, a, a):

$x_{c m} = \frac{8 m \cdot \frac{a}{2} - m \cdot a}{7 m} = \frac{3 a}{7}$ , and by symmetry $y_{c m} = z_{c m} = \frac{3 a}{7}$ .

Answer: (B) $(\frac{3 a}{7}, \frac{3 a}{7}, \frac{3 a}{7})$

Physics - Center of Mass Question with Solution | TestHub

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