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Units and Measurement question

2025 · Q164
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Units and Measurement question

2025 · Q164

NEETPhysicsUnits and MeasurementMCQ+4 / −1

A balloon is made of a material of surface tension SSS and its inflation outlet (from where gas is filled in it) has small area AAA. It is filled with a gas of density ρ\rhoρ and takes a spherical shape of radius RRR. When the gas is allowed to flow freely out of it, its radius rrr changes from RRR to 0 (zero) in time TTT. If the speed v(r)v(r)v(r) of gas coming out of the balloon depends on rrr as rαr^\alpharα and T∝SαAβργRδT \propto S^\alpha A^\beta \rho^\gamma R^\deltaT∝SαAβργRδ then

  1. A
    a=−12,α=−12,β=−1,γ=12,δ=72a=-\frac{1}{2}, \alpha=-\frac{1}{2}, \beta=-1, \gamma=\frac{1}{2}, \delta=\frac{7}{2}a=−21​,α=−21​,β=−1,γ=21​,δ=27​
  2. B
    a=12,α=12,β=−12,γ=12,δ=72a=\frac{1}{2}, \alpha=\frac{1}{2}, \beta=-\frac{1}{2}, \gamma=\frac{1}{2}, \delta=\frac{7}{2}a=21​,α=21​,β=−21​,γ=21​,δ=27​
  3. C
    a=12,α=12,β=−1,γ=+1,δ=32a=\frac{1}{2}, \alpha=\frac{1}{2}, \beta=-1, \gamma=+1, \delta=\frac{3}{2}a=21​,α=21​,β=−1,γ=+1,δ=23​
  4. D
    a=−12,α=−12,β=−1,γ=−12,δ=52a=-\frac{1}{2}, \alpha=-\frac{1}{2}, \beta=-1, \gamma=-\frac{1}{2}, \delta=\frac{5}{2}a=−21​,α=−21​,β=−1,γ=−21​,δ=25​
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