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# Velocity v  of wave produced in the water depends on the wave length lamda (L) density of water d and acceleration due to gravity g relation betweeen these quantities will be

147 Points
11 years ago

Dear pallavi

This is a problem of dimention

let

V = k λadbgc

where k ,a,b,c are constant

Now write the dimension of all the quantities

[ M0 L1 T-1]  = [L1]a[ M1 L-3]b [L1 T-2]c

[ M0 L1 T-1]  = [ Mb L-3b+a+c  T-2c]

compair

b=0

-2c=-1   or c=1/2

and  -3b +a+c =1

a =1/2

so V =k(λg)1/2

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