Question

to answer this question, first click here to view the associated video. two particles are located on the x - axis as shown. particle 1 has a mass 3m, and particle 2 has a mass of m. where on the x - axis, as indicated by the letters a, b, c, and d, is closest to the center of mass of this system?

Explanation:

Step1: Recall the formula for center of mass

The formula for the \(x\) - coordinate of the center of mass of a two - particle system is \(x_{cm}=\frac{m_1x_1 + m_2x_2}{m_1 + m_2}\). Let's assume the position of the particle with mass \(3m\) is \(x_1 = 0\) (for simplicity, since we are interested in the relative position). Let the distance between each adjacent mark on the \(x\) - axis be \(d\). Then the position of the particle with mass \(m\) is \(x_2=7d\).

Step2: Calculate the center of mass

Substitute \(m_1 = 3m\), \(x_1 = 0\), \(m_2=m\) and \(x_2 = 7d\) into the formula \(x_{cm}=\frac{m_1x_1 + m_2x_2}{m_1 + m_2}\).

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If we assume the position of particle \(1\) (mass \(3m\)) is at \(x = 0\), and each interval is of length \(d\). Then \(x_{cm}=1.75d\) which is closest to point \(B\) (assuming the first mark after the particle \(1\) is \(A\) at \(d\), \(B\) at \(2d\)).

Answer:

B