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  • 45. The speed of a wave produced in water is given by   <img alt="u=\lambda^{a}g^{b}p^{c}" src="https://entrancecorner.oncodecogs.com/gif.latex?u%3D%5Clambda%5E%7Ba%7Dg%5E%7Bb%7Dp%5E%7Bc%

45. The speed of a wave produced in water is given by   u=\lambda^{a}g^{b}p^{c}  . Where \lambda, g and 
are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are :

Option: 1

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


Option: 2

1,-1,0


Option: 3

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


Option: 4

1,1,0


Answers (1)

best_answer

By dimensional analysis,

V=\lambda^{a}g^{b}p^{c}

\begin{aligned} & {\left[L^1 T^{-1}\right]=\left[L^1\right]^{\mathrm{a}}\left[\mathrm{L}^1 T^{-2}\right]^b\left[M^1 L^{-3}\right]^c} \\ & {\left[L^1 T^{-1}\right]=\left[M^c L^{a+b-3 c} T^{-2 b}\right]} \end{aligned}

On comparing respective powers,

c=0,-2b=-1\, ,a+b-3c=1,

b=\frac{1}{2},a=\frac{1}{2},

Posted by

Nehul

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