Question bank/NEET UG/Physics

NEET UGPhysicsModerateNEET 2025

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\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)v(r) of gas coming out of the balloon depends on r as rar^a and T∝SαAβργRδT \propto S^\alpha A^\beta \rho^\gamma R^\delta then

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Sol. T∝SαAβργRδT \propto S^\alpha A^\beta \rho^\gamma R^\delta

M0L0T1=K(MT−2)α(L2)β(ML−3)γLδM^0L^0T^1 = K(MT^{-2})^\alpha (L^2)^\beta (ML^{-3})^\gamma L^\delta

M0L0T1=K[Mα+γL2β−3γ+δT−2α]M^0L^0T^1 = K[M^{\alpha + \gamma} L^{2\beta - 3\gamma + \delta} T^{-2\alpha}]

−2α=1α=−12-2\alpha = 1 \quad \alpha = -\frac{1}{2}

α+γ=0γ=12\alpha + \gamma = 0 \quad \gamma = \frac{1}{2}

2β−3γ+δ=02\beta - 3\gamma + \delta = 0

2β−3(12)+δ=02\beta - 3(\frac{1}{2}) + \delta = 0

By hit and trial (using option (1))

Put β=−1\beta = -1

2(−1)−32+δ=0∴δ=722(-1) - \frac{3}{2} + \delta = 0 \quad \therefore \delta = \frac{7}{2}

Source: geekyrakshit/indian-exam-questions / neet2025-code45

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