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? c d b a

Explanation:

Step1: Assume the position of particle 1 and particle 2

Let the position of particle 1 (\(m_1 = 3m\)) be \(x_1=0\) (for simplicity of calculation, we can set the position of the left - hand particle as the origin). Let the distance between the two particles be \(d = 6\) units (counting the number of intervals between them in the diagram). Then the position of particle 2 (\(m_2 = 2m\)) is \(x_2 = 6\).

Step2: Use the formula for the center of mass

The formula for the \(x\) - coordinate of the center of mass of a two - particle system is \(x_{cm}=\frac{m_1x_1 + m_2x_2}{m_1 + m_2}\).
Substitute \(m_1 = 3m\), \(x_1 = 0\), \(m_2=2m\), and \(x_2 = 6\) into the formula:

$$
LATEXBLOCK0
$$

If we consider the scale of the diagram (assuming each interval has a length of 1 unit), starting from particle 1 (\(x = 0\)), a value of \(x = 2.4\) is closest to point \(B\) (since \(A\) is at \(x = 1\), \(B\) is at \(x = 2\), \(C\) is at \(x = 4\), \(D\) is at \(x = 5\)).

Answer:

C. B