A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has a small area A. It is filled with a gas of density \rho and takes a spherical shape o

Question

A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has a small area $A$ . It is filled with a gas of density $ρ$ 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 in time $T$ . If the speed $v (r)$ of the gas coming out of the balloon depends on $r$ as $r^{a}$ and $T \propto S^{α} A^{β} ρ^{γ} R^{δ}$ , then:

Question 24 as printed in the NEET 2025 booklet

![Question 24 as printed in the NEET 2025 booklet](/figures/neet-2025/q24.png)

Vishal Gupta · Accepted Answer

C. The excess pressure \dfrac{4S}{R} drives the outflow, so v \sim \sqrt{\dfrac{S}{ho r}}, giving a = -	frac12. Time to empty \sim \dfrac{	ext{volume}}{Av} \sim \dfrac{R^3}{A}\sqrt{\dfrac{ho R}{S}} = S^{-1/2} A^{-1} ho^{1/2} R^{7/2}: \alpha = -	frac12, \beta = -1, \gamma = 	frac12, \delta = 	frac72.

Units and Measurements

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