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Question
A body has its centre of mass at the origin. the x-coordinates of the particles
(a) may be all positive
(b) may be all negative
(c) may be all non-negative
(d) may be positive for some cases and negative in other cases.
Solution
(c) may be all non-negative
(d) may be positive for some cases and negative for other cases
According to the question, the centre of mass is at origin.
\[\therefore\] \[X = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3 + . . .}{m_1 + m_2 + m_3 + . . . . . . .} = 0\]
\[\Rightarrow m_1 x_1 + m_2 x_2 + m_3 x_3 + . . . = 0\]
From the above equation, it can be concluded that all the x-coordinates may be non-negative.
In other words, they may be positive for some cases and negative for others.
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