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Question: The velocity v of waves produced in water depends on their wavelength l, the density of water r, and...

The velocity v of waves produced in water depends on their wavelength l, the density of water r, and acceleration due to gravity g. The square of velocity is proportional to –

A

λ−1g−1ρ−1\lambda^{- 1}g^{- 1}\rho^{- 1}

B

lg

C

lrg

D

λ2g−2ρ−1\lambda^{2}g^{- 2}\rho^{- 1}

Answer

lg

Explanation

Solution

v∝λaρbgc⇒LT−1=La(ML−1T−2)(LT−2)cv \propto \lambda^{a}\rho^{b}g^{c} \Rightarrow LT^{- 1} = L^{a}\left( ML^{- 1}T^{- 2} \right)\left( LT^{- 2} \right)^{c}

a – b + c = 1 …(i)

b = 0 …(ii)

–2b – 2c = –1 …(iii)