Answer:
a) The center of mass of the system composed of particles of masses m₁ and m₂, is located at a distance longer than 5 m and less than 10 m.
Explanation:
For a group of point masses, located along a straight line, we know, first of all, that the center of mass must be located on this line, as the y-coordinate of the center of mass is 0, due to no mass has a y-coordinate ≠ 0.
If we know that m₁ < m₂, we can choose to put m₁ just in the origin, so his x-coordinate, is 0 also.
With these premises, we can find mathematically the center of mass as follows:
Xcm = x₂*m₂ / (m₁+m₂)
So, as m₂/m₁+m₂ < 1, the x-coordinate of the center of mass must be located to the left of m₂.
An obvious question arises : How much to the left?
If (in the limit) m₁ =m₂, the factor m₂/ m₁+m₂ would be exactly 1/2.
⇒ Xcm = 1/2 * X₂ = 0.5* 10 m = 5 m
If m₁ < m₂, the center of mass will be more to the right (closer to m₂) than in the limit case when m₁=m₂, so it will be located at a distance longer than 5 m, and less than 10 m (which would be the case for m₁=0).
