Question

An air bubble inside water oscillates due to some explosion with period T. If $T\propto P^a{d}^b{E}^c$ then determine the values of a,b and c. Here P, d and E are the static pressure, density and total energy of explosion of water, respectively.

• A. $a=\frac{5}{6}$, $b=1$, $c=\frac{1}{3}$
• B. $a=-\frac{5}{6}$, $b=\frac{1}{2}$, $c=\frac{1}{3}$
• C. $a=1,b=1,c=1$
• D. $a=0,b=0,c=1$

Answer 1

The correct option is B $a=-\frac{5}{6}$, $b=\frac{1}{2}$, $c=\frac{1}{3}$

$T={\left(M{L}^{-1}{T}^{-2}\right)}^a{\left(M{L}^{-3}\right)}^b{\left(M{L}^2{T}^{-2}\right)}^c$

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

Solving these, we get $b=1/2,c=1/3,a=-5/6$