NEET 2025 · PhysicsExcess pressurePrevious 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 flows freely out, its radius r changes from R to 0 in time T. If the speed v(r) of gas coming out depends on r as rᵅ and T ∝ Sᵝ Aᵞ Rᵟ ρᵋ, then:
Answer: (A) α = −1/2, β = −1/2, γ = −1, δ = 7/2, ε = 1/2. Excess (Laplace) pressure ∝ S/r drives efflux: ½ρv² ~ S/r ⇒ v ∝ (S/(ρr))^{1/2}, so α = −1/2.
- A.α = −1/2, β = −1/2, γ = −1, δ = 7/2, ε = 1/2✓
- B.α = 1/2, β = 1/2, γ = −1/2, δ = 1/2, ε = 7/2
- C.α = 1/2, β = 1/2, γ = −1, δ = 1, ε = 3/2
- D.α = −1/2, β = −1/2, γ = −1, δ = −1/2, ε = 5/2
Correct Answer
(A) α = −1/2, β = −1/2, γ = −1, δ = 7/2, ε = 1/2
Solution & Explanation
Excess (Laplace) pressure ∝ S/r drives efflux: ½ρv² ~ S/r ⇒ v ∝ (S/(ρr))^{1/2}, so α = −1/2. Volume outflow rate A·v empties the balloon: T ~ R³/(A·v(R)) with v(R) ∝ (S/(ρR))^{1/2}. Dimensional/scaling bookkeeping gives β = −1/2, γ = −1, δ = 7/2, ε = 1/2 (option a).
🎯
43,000+ questions in हिंदी & English · one-tap toggle
Open →📚Practice all NEET Physics PYQs chapter-wise →💡Don't get it? Learn the Mechanical Properties Of Fluids concepts →Practice NEET 2025 Physics — free, with instant solutions
43,000+ NEET questions solved step-by-step, chapter-wise, in the MedicNEET app.
More NEET PYQ solutions
PhysIf a soap bubble expands, the pressure inside the bubble:PhysA soap bubble of radius 1 mm is blown from a detergent solution of surface tension 2.5 × 10⁻² N m⁻¹. The pressure inside the bubble equals the pressure at a point Z₀ below the free surface of water in a container. Taking g = 10 m s⁻² and density of water = 10³ kg m⁻³, the value of Z₀ is:PhysAn electric dipole with dipole moment 5 × 10⁻⁶ C·m is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is:PhysTwo identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (radii negligible vs separation, treated as point charges) is best given as:PhysThe plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K1 and K2 with thickness 3d/8 and d/2 respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K1/K2 = 1.25, the value of K1 is:PhysA sphere of radius R is carved out of a uniform solid sphere of radius 2R (internally tangent, so its centre is at distance R from the big centre). The ratio of the moment of inertia of the small sphere to that of the remaining part, both about the Y-axis through the big sphere's centre, is:PhysThe Sun rotates once in 27 days. If it expanded to twice its present radius (uniform-density sphere, no external influence), its new period would be about:PhysA uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall, making 60° with the wall; its lower end rests on a rough horizontal floor. The friction force exerted by the floor is: (g = 10 m/s²)