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Consider the Law of Gravitation where the force of gravity F is:
F = G(m1m2/r2)
Which of the following represents the gravitational constant G in the fundamental dimensions of mass (M), length (L) and time (T)?
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Correct Answer: A. M-1L3T-2
PHY 2.4
This is a classic example of dimensional analysis (DA). Expect to use DA to one degree or the other during the real MCAT. First, you should know that the unit of force is a newton which is also a kg m/s2 (even if you did not memorize that, it is easy to work out since F = ma so the units of F must be kg multiplied by acceleration which is m/s2). Of course the 2 m’s in the Law of Gravitation represent masses (M) and the r represents a distance or length (L). So we get:
F = G(m1m2/r2)
Now transferring to the fundamental quantities except for G:
MLT-2 = G(M)2L-2
Divide both sides by (M)2L-2 and isolate for G:
G = M-1L3T-2
… which is the same as m3kg-1s-2.
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