Question

ans please. please please please​

Answer 1

Given :

Velocity of water waves v depend upon wavelength (λ), density (ρ) and acceleration due to gravity (g)$.$

To Find :

We have to find relation between these quantities$.$

Solution :

◈ Dimension Formula :

$\bigstar\sf\:v=[L^1T^{-1}]$

$\bigstar\sf\:\lambda=[L^1]$

$\bigstar\sf\:\rho=[M^1L^{-3}]$

$\bigstar\sf\:g=[L^1T^{-2}]$

ATQ,

$\mapsto\bf\:v\propto[\lambda]^{x}[\rho]^{y}[g]^{z}$

$\mapsto\sf\:[L^1T^{-1}]\propto[L^1]^x[M^1L^{-3}]^y[L^1T^{-2}]^z$

$\mapsto\sf\:[L^1T^{-1}]\propto[M^yL^{x-3y+z}T^{-2z}]$

Therefore,

• y = 0
• x - 3y + z = 1
• -2z = -1 ➝ z = 1/2

_________________________________

⇒ x - 3y + z = 1

⇒ x - 3(0) + (1/2) = 1

⇒ x - 0 - (1/2) = 1

⇒ x = 1/2

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$\mapsto\sf\:v\propto\lambda^{\frac{1}{2}}\rho^0g^{\frac{1}{2}}$

$\mapsto\sf\:v\propto\sqrt{\lambda g}$

$\mapsto\underline{\boxed{\bf{\purple{v^2\propto\lambda g}}}}$

Option - C is the correct answer.