1.

The velocity of water wave `v` may depend on their wavelength `lambda`, the density of water `rho` and the acceleration due to gravity `g`. The method of dimensions gives the relation between these quantities asA. `v^(2) prop lambda g rho`B. `v^(2) prop lambda^(-1) g^(-1) rho^(-1)`C. `v^(2) prop g lambda`D. `v^(2) prop rho lambda`

Answer» Correct Answer - C
(3) `v prop lambda^(a) rho^(b) g^(c )`
`LT^(-1) prop [L]^(a) [ML^(-3)]^(b) [LT^(-2)]^(c )`
`M^(0) L^(1) T^(-1) prop M^(b) L^(a - 3b + c) T^(-2c)`
Comparing powers of `M, L` and `T`
`b = 0`
`a - 3b + c = 1`
`- 2c = - 1 implies c = (1)/(2)`
`v prop lambda^(1//2) g^(1//2)`
`v^(2) prop lambda g`


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