NEET 2025 — Physics solution

NEET2025Physics

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 $ρ$ and takes a spherical shape of radius $R$ . When the gas is allowed to flow freely out of it, its radius 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 $r^{a}$ and $T \propto S^{α} ρ^{β} A^{γ} R^{δ}$ then:

A
$a = \frac{1}{2}, α = - \frac{1}{2}, β = - 1, γ = + 1, δ = \frac{3}{2}$
B
$a = - \frac{1}{2}, α = - \frac{1}{2}, β = - 1, γ = - \frac{1}{2}, δ = \frac{5}{2}$
C
$a = - \frac{1}{2}, α = - \frac{1}{2}, β = - 1, γ = \frac{1}{2}, δ = \frac{7}{2}$
D
$a = \frac{1}{2}, α = \frac{1}{2}, β = - \frac{1}{2}, γ = \frac{1}{2}, δ = \frac{7}{2}$

Solution

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