Answer to Question #95948 in Classical Mechanics for Fifi

Question #95948
Using only the constants G = 6.67 x 10^-11 m^3/kg/s^2 and c = 3.00 x 10^8 m/s and dimensional analysis, estimate the peak power that was emitted in gravitational waves recently detected by LIGO from two merging black holes. (Hint: the SI unit of power is a watt, 1 W = 1 kg m^2 s^-3.) [3 marks]
1
Expert's answer
2019-10-07T10:47:29-0400
"P=G^xc^y"

"kg\\cdot m^2\\cdot s^{-3}=(kg^{-1}\\cdot m^3\\cdot s^{-2})^x(m\\cdot s^{-1})^y"

Thus,


"1=-x\\to x=-1"

"2=3(-1)+y\\to y=5"

Thus,


"P=G^{-1}c^5=(6.67\\cdot 10^{-11})^{-1}(3\\cdot 10^8)^5=3.64\\cdot 10^{52}W"


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