To find the coordinates of the center of mass for two objects with masses \( m_1 \) and \( m_2 \), and distances \( L_1 \) and \( L_2 \) from a chosen origin or reference point, we use the concept that the ratio of their distances from the center of mass is equal to the inverse of the ratio of their masses. This is mathematically expressed as:
[tex]\[
\frac{L_1}{L_2} = \frac{m_2}{m_1}
\][/tex]
However, in this instance, crucial details such as the specific values for the masses (\( m_1 \) and \( m_2 \)) and the distances (\( L_1 \) and \( L_2 \)) are not provided. Without these values, we cannot compute the exact coordinates of the center of mass.
To formally proceed, the general form to locate the center of mass \( x_{cm} \) along a straight line should be:
[tex]\[
x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}
\][/tex]
where \( x_1 \) and \( x_2 \) are the positions of object 1 and object 2, respectively.
Without the specific values for \( m_1 \), \( m_2 \), \( x_1 \), and \( x_2 \), it is not possible to determine the precise coordinates of the center of mass.
Therefore, to solve for the coordinates of the center of mass, additional information about the masses and distances or positions involved is required. In the absence of such data, the problem remains under-defined.
