Can You Solve This Amazing "Deflating" Balloon Problem From INPhO 2022 скачать в хорошем качестве

Can You Solve This Amazing "Deflating" Balloon Problem From INPhO 2022

In this Physics video in Hindi for the chapter : "Mechanical Properties of Solids" and "Mechanical Properties of Fluids" of Class 11, we discussed a Previous Years' Question of INPhO 2022 that is extremely important for students preparing for the Indian National Physics Olympiad, higher stages of the Indian National Physics Olympiad, and advanced competitive examinations such as IIT JEE Advanced, where interdisciplinary thinking from the chapters Mechanical Properties of Solids and Mechanical Properties of Fluids is strongly emphasized. Question : Consider an air filled spherical balloon comprised of elastic material of surface tension γ = 500 kg/s². The pressure outside the balloon is the atmospheric pressure (P_atm = 101 kPa) and the density of air outside is ρ_atm = 1.22 kg/m³. The balloon starts deflating slowly. Assume that the average velocity of air inside the balloon is negligible, and air leaves the balloon in a streamline fashion. Consider γ to be constant throughout, and the air to be incompressible. (a) [8 marks] Write an expression for the time t required to deflate the balloon through a small opening of cross-sectional area A from an initial radius R₀ to a final radius R. (b) [1 marks] Obtain the value of this time for A = 1 × 10⁻⁵ m², R₀ = 0.15 m, and R = 0.05 m. 👇 👇 👇 👇 👇 👇 Related Playlists 👇 👇 👇 👇 👇 👇 👇 👇 👇 THIS Playlist : INPhO - PYQ    • Indian National Physics Olympiad - PYQ   Playlist on : Aptitude Test Problems in Physics, S.S. Krotov    • Krotov's "Mechanics"   Playlist on : Jaan Kalda's Handout for Mechanics    • Jaan Kalda's "Mechanics" for Physics Olymp...   Playlist on : Fluids - Pathfinder    • Fluids : Pathfinder   Playlist on : JEE Advanced PYQ (Mechanical Properties of Fluids)    • Fluids : JEE Advanced PYQ   ☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️☝️ This INPhO 2022 problem beautifully integrates ideas from both Mechanical Properties of Solids and Mechanical Properties of Fluids, making it a classic example of the level of reasoning expected in the Indian National Physics Olympiad. In the solution approach explained in the video, we first analyze the mechanical equilibrium of the balloon membrane by relating the pressure difference across the elastic surface to the surface tension, an idea rooted in the chapter Mechanical Properties of Solids. Next, concepts from Mechanical Properties of Fluids are applied to understand how air flows out of the balloon through a small opening under a pressure difference, assuming steady and streamlined flow. By combining the pressure condition at the balloon surface with energy considerations for fluid flow, the rate at which the radius of the balloon changes is determined. This rate is then connected to the gradual decrease in volume of the balloon, allowing the total time of deflation to be obtained by summing the contributions over the entire change in radius. The numerical part is handled by substituting the given values and interpreting the final result physically, a style of reasoning that is repeatedly rewarded in the Indian National Physics Olympiad. This problem highlights how Mechanical Properties of Solids and Mechanical Properties of Fluids are not isolated chapters, but are deeply connected when analyzing real physical systems such as elastic balloons, which is why such problems are a favorite in the Indian National Physics Olympiad. Surface tension is a physical quantity defined as the force acting per unit length along the surface of a liquid or elastic membrane, and in this problem it determines how the elastic balloon resists deformation due to the pressure difference across its surface, a key idea from Mechanical Properties of Solids. Pressure is defined as the normal force exerted per unit area by a fluid on a surface, and in this question the difference between internal and external pressure governs the outflow of air, making it central to the application of Mechanical Properties of Fluids in Indian National Physics Olympiad problems. The principle of conservation of energy states that energy cannot be created or destroyed but can only be transformed from one form to another, and here it is used to relate the pressure energy of the air inside the balloon to the kinetic energy of the air flowing out through the opening. The continuity principle of fluid flow states that for an incompressible fluid flowing steadily, the mass flow rate remains constant across any cross-section of the flow, and this principle is crucial for linking the rate of air outflow to the gradual decrease in the balloon’s volume in this Indian National Physics Olympiad question.