Question

Two point particles, with masses m and 2 m, are separated by some distance Lin an uniform gravitational field. The center of gravity of this two particle system is:________
А. located L/2 distance away from either mass and on the line joining the two particles.
B. located 1/3 distance away from 2 m and on the line joining the two particles.
C. located L/4 distance away from 2 m and on the line joining the two particles.
D. located L/3 distance away from mand on the line joining the two particles.
E. located L/4 distance away from m and on the line joining the two particles.
F. located where the mass 2 m is located.

Answer 1

The center of gravity of this two particle system is located 1/3 distance away from 2 m and on the line joining the two particles.

The given parameters:

• Mass of the first particle, = m
• Mass of the second particle, = 2m
• Distance between the two particles, = L

The center of gravity of the two particles when first particle is fixed is calculated as;

$C_G = \frac{m(0 ) \ +2m(L) }{m+ 2m} \\\\C_G = \frac{2mL}{3m} \\\\C_G = \frac{2L}{3}$

The center of gravity of the two particles when second particle is fixed is calculated as;

$C_G = \frac{m(L) \ + \ 2m(0)}{m + 2m} \\\\C_G = \frac{mL}{3m} \\\\C_G = \frac{L}{3}$

Thus, the center of gravity of this two particle system is located 1/3 distance away from 2 m and on the line joining the two particles.

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