A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius $r$ changes from $R$ to $0$ (zero) in time $T$. If the speed $v(r)$ of gas coming out of the balloon depends on $r$ as $r^{\alpha }$ and $T\propto S^a{A}^{\beta }{\rho }^{\gamma }{R}^{\delta }$ then:

1. A
   $a=\frac{1}{2},\alpha =\frac{1}{2},\beta =-1,\gamma =+1,\delta =\frac{3}{2}$
2. B
   $a=-\frac{1}{2},\alpha =-\frac{1}{2},\beta =-1,\gamma =-\frac{1}{2},\delta =\frac{5}{2}$
3. C
   $a=-\frac{1}{2},\alpha =\frac{1}{2},\beta =-1,\gamma =\frac{1}{2},\delta =\frac{7}{2}$
4. D
   $a=\frac{1}{2},\alpha =\frac{1}{2},\beta =-1,\gamma =\frac{1}{2},\delta =\frac{7}{2}$