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`
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 as
Juhi Sawhney
Asked: 3 years ago2022-11-10T07:48:17+05:30
2022-11-10T07:48:17+05:30In: General Awareness
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 as
A. `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`
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 as
A. `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`
A. `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`
Leave an answer
Leave an answer
Sheetal Minhas
Asked: 3 years ago2022-11-06T21:29:57+05:30
2022-11-06T21:29:57+05:30In: General Awareness
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 as
A. `V^(2) prop g^(-1) gamma^(-1)`
B. `V^(2) prop g lambda`
C. `V^(2) prop g lambda rho`
D. `V^(2) prop g^(-1) lambda^(-3)`
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 as
A. `V^(2) prop g^(-1) gamma^(-1)`
B. `V^(2) prop g lambda`
C. `V^(2) prop g lambda rho`
D. `V^(2) prop g^(-1) lambda^(-3)`
A. `V^(2) prop g^(-1) gamma^(-1)`
B. `V^(2) prop g lambda`
C. `V^(2) prop g lambda rho`
D. `V^(2) prop g^(-1) lambda^(-3)`
Leave an answer
Leave an answer
-
Correct Answer – b
See question 38 above.
`v prop sqrt(g lambda)rArr v^(2) prop g lambda`
Correct Answer – `v=ksqrt(lambdag)`