Question

The time period of a soap bubble is it which depends on pressure density and surface tension then the relation of T is?​

Answer 1

 ... on pressure ,density and surface tension then the relation for… ... the time period of a soap bubble which depends on ... Time taken by bomb to hit the ground.

Answer 2

Answer:

Required relation is $T \propto (\frac{\rho r^3}{S} )^{\frac{1}{2}$

Explanation:

Let,   $T \propto \rho^\alpha r^\beta S^\gamma$

⇒ $[T ]\propto [\rho]^\alpha[ r]^\beta [S]^\gamma$

Now writing in terms M,L,T ,

$[T ]\propto [M^1 L^{-3}T^0]^\alpha[ M^0 L^1T^0]^\beta [M^1L^0T^{-2}]^\gamma$

$or, [M^0 L^0 T^1] = [M^{\alpha +\gamma }L^{-3\alpha+\beta}T^{-2\gamma}]$

Comparing the exponents on both sides,

$\alpha +\gamma =0$   → $\alpha =-\gamma$

$-3\alpha +\beta =0$   → $\beta = 3\alpha$

$-2 \gamma =1$      → $\gamma= - \frac{1}{2}$

∴Required relation is

                                        $[T ]\propto [\rho]^\frac{1}{2} [ r]^\frac{3}{2} [S]^{ -\frac{1}{2}$\

                                     →      $T \propto (\frac{\rho r^3}{S} )^{\frac{1}{2}$