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An important milestone in the evolution of the universe just after the big bang is the Planck time t^(p), the value of which deponds on three fundamental constants-speed c of light in vacuum, gravitational constant G and Planck's constant h. Then, t_(p)prop |
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Answer» `GHC^(5)` `M^(0)L^(0)T^(1)prop[L^(1)T^(-1)]^(x)[M^(-1)L^(3)T^(-2)]^(y)xx[ML^(2)T^(-1)]^(z)propM^(-y+z)xxL^(x+3y+2z)XXT^(-x-2y-z)` `:.-y+z=0|x+3y+2z=0|` and `-x-2y-z=1` or `{:(y=3),("or"),(z=(1)/(2)):}|{:(x+5y=0),(x=-5y),(x=-(5)/(2)):}|{:(-x-3y=1),(5y-3y=1),(y=(1)/(2)):}` `:.t_(p)alphaG^((1)/(2))h^((1)/(2))c((-5)/(2))=[(Gh)/(c^(5))]^((1)/(2))` Hence `T^(2)=4pi^(2).(L)/(g)` or `g=(4pi^(2)L)/(T^(2))`. |
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