Q. Frequency is the function of density $(\rho)$ , length $(a)$ and surface tension $(T)$. Then its value is
A) $k\rho^{1/2}a^{3/2}/\sqrt{T}$
B) $k\rho^{3/2}a^{3/2}/\sqrt{T}$
C) $k\rho^{1/2}a^{3/2}/T^{3/4}$
D) None of these
Explanation
Let $n = k\rho^{a}a^{b}T^{c}$ where $\lbrack\rho\rbrack = \left\lbrack ML^{- 3} \right\rbrack,\ \lbrack a\rbrack = \lbrack L\rbrack$ and $\lbrack T\rbrack = \left\lbrack MT^{- 2} \right\rbrack$ Comparing dimensions both sides we get $a = \frac{- 1}{2},\ b = \frac{- 3}{2}$ and $c = \frac{1}{2}\ \therefore\eta = k\rho^{- 1/2}a^{- 3/2}T^{- 1/2}$ $= \frac{K\sqrt{T}}{\rho^{1/2}a^{3/2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.