NEET 2025 · PhysicsPrevious Year Question
A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled) 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 r changes from R to 0 in time T. If the speed v(r) of gas coming out depends on r as r^a and T ∝ S^α A^β ρ^γ R^δ, then:
- A.a=-1/2, α=-1/2, β=-1, γ=1/2, δ=7/2✓
- B.a=1/2, α=1/2, β=-1/2, γ=1/2, δ=7/2
- C.a=1/2, α=1/2, β=-1, γ=+1, δ=3/2
- D.a=-1/2, α=-1/2, β=-1, γ=-1/2, δ=5/2
Correct Answer
(A) a=-1/2, α=-1/2, β=-1, γ=1/2, δ=7/2
Solution & Explanation
Correct Answer (A): a=-1/2, α=-1/2, β=-1, γ=1/2, δ=7/2 T ∝ S^α A^β ρ^γ R^δ with [S]=MT⁻², [A]=L², [ρ]=ML⁻³, [R]=L. Matching M: α+γ=0; T: -2α=1→α=-1/2, γ=1/2; with a=-1/2 and δ=7/2, L: 2β-3γ+δ=0→β=-1.
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