The speed of a wave produced in water is give | vedclass

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Question

$v=\lambda^a g^b \rho^c$

using dimension formula

$\Rightarrow\left[ M ^0 L ^1 T ^{-1}\right]=\left[ L ^1\right]^{ a }\left[ L ^1 T ^{-2}\right]^

Vedclass · Accepted Answer

$\frac{1}{2}, \frac{1}{2}, 0$

Vedclass · Answer

$v=\lambda^a g^b ho^c$

using dimension formula

$\Rightarrow\left[ M ^0 L ^1 T ^{-1}ight]=\left[ L ^1ight]^{ a }\left[ L ^1 T ^{-2}ight]^{ b }\left[ M ^1 L ^{-3}ight]^{ c }$

$\Rightarrow\left[ M ^0 L ^1 T ^{-1}ight]=\left[ M ^{ c } L ^{ a + b -3 c } T ^{-2 b}ight]$

$	herefore c =0, a + b -3 c =1,-2 b =-1 \Rightarrow b =\frac{1}{2}$

Now $a+b-3 c=1$

$\Rightarrow a+\frac{1}{2}-0=1$

$\Rightarrow a=\frac{1}{2}$

$	herefore a=\frac{1}{2}, b=\frac{1}{2}, c=0$

The speed of a wave produced in water is given by $v=\lambda^a g^b \rho^c$. Where $\lambda$, g and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a , b$ and $c$ respectively, are

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