Question

A gas bubble forms an explosion under water which oscillate with a period $T\propto p^a{\rho }^b{E}^c,$ where p is the static pressure, p is the density of water and E is the total energy of explosion. Then, the values of q, b and c will be

• A. $-\frac{5}{6},\frac{1}{2},\frac{1}{3}$
• B. $\frac{2}{5},\frac{1}{3},\frac{1}{4}$
• C. $\frac{4}{5},\frac{9}{8},\frac{1}{4}$
• D. $\frac{3}{2},\frac{1}{4},\frac{5}{6}$

Answer 1

Answer: (A)

As $T\propto P^a{\rho }^b{E}^c$ From principle of homogeneity $[T]={[M{L}^{-1}{T}^{-2}]}^a{[M{L}^{-3}]}^b{[M{L}^2{T}^{-2}]}^c$ $[M^0{L}^0{T}^1]=[M^{a+b+c}{L}^{-a-3b-2c}{T}^{-2a-3b-2c}]$ Equating the exponents $a+b+c=0,$ $-a-3b-2c=0$ and $-2a-3b-2c=1$ Solving these equations, we get $a=-\frac{5}{6},b=\frac{1}{2}$ and $c=\frac{1}{3}$