Q 11-01-137JEE MainJEE Main 2023 (15 Apr, Shift 1)Medium
The speed of a wave produced in water is given by $v=\lambda^ag^b\rho^c$, where $\lambda$, $g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a$, $b$ and $c$ respectively are
Answer: (D) $\frac12,\ \frac12,\ 0$
$[\text{LT}^{-1}]=[\text{L}]^a[\text{LT}^{-2}]^b[\text{ML}^{-3}]^c$.
M: $c=0$; T: $-2b=-1\Rightarrow b=\tfrac12$; L: $a+b-3c=1\Rightarrow a=\tfrac12$.
Solution by Sreeraj P, M.Sc Physics