the velocity 'v' of water waves may depend on their wavelength, density of water and acceleration due to gravity. Find relation between these quantities by the method of dimension

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let velocity be "v"=[LT-1]              let wave lenght be  "a"=[L]     let density  be "b"=[ML3]      let acc. due to gravity be "g" =[LT-2]

v = k ax b y g z    

[M0LT-1]      =[L]x [ML3]y   [LT-2]z

[M0LT-1]      =[M]y [L]x+3y-2z  [T]-2z 

equate M,L,T...

M0  = M y  .....        so y=0

[T-1]      =  [T]-2z                   so     -1=-2z........        z=1/2

[L] = [L]x+3y-2z                

1=x-1        so  x =2 

thus        v = k ax b y g z      

 wher   x=2     y=0   z =1/2

       m nt able to put square n ol......


  • -2

 density is ML -3 not +3

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