Скачать или смотреть I Made This Hard Problem Harder | "Chain Sliding" Problem from IRODOV 1.107

In this video, we are solving a very interesting and advanced problem from the book Problems in General Physics by I.E. Irodov. This is Question Number 1.107 from the chapter Laws of Motion. The complete solution is explained in Hindi, so that students preparing for competitive exams like IIT-JEE can clearly understand each and every step of the reasoning. This problem belongs to the category of conceptual mechanics problems that are often seen in IIT-JEE Advanced level examinations.

The question states: A chain of length l is placed on a smooth spherical surface of radius R with one of its ends fixed at the top of the sphere. What will be the acceleration w of each element of the chain when its upper end is released? It is assumed that the length of the chain l is less than half of the circumference of the sphere.

To solve this, we start by visualizing the physical setup of the chain resting on a smooth spherical surface. When the upper end is released, every element of the chain will experience acceleration due to gravity. Since the surface is smooth, there is no friction, and only normal and tangential components of forces come into play. The task is to determine the effective acceleration of the chain elements when the constraint at the top is removed.

The key to solving this problem lies in using symmetry arguments and analyzing the distribution of forces along the spherical surface. Each small part of the chain will experience tangential acceleration along the surface of the sphere. By considering the entire chain and its center of mass, one can calculate the net acceleration imparted to the chain. The assumption that the chain length is less than half the semicircle ensures that the chain does not wrap around the sphere and that the analysis remains valid.

This problem beautifully illustrates the power of concepts from the chapter Laws of Motion. Instead of direct force equations alone, we rely on center of mass motion, constraints of smooth contact, and the relationship between gravity and surface reactions. By carefully applying these ideas, we determine the exact value of acceleration of each element.

For students preparing for IIT-JEE Advanced, this problem is a must practice. It not only tests understanding of tangential and normal components of motion on curved surfaces but also improves logical reasoning and problem-solving skills. The chapter Laws of Motion has many such applications where acceleration is determined by combining geometric constraints with Newtonian mechanics.

By the end of this video, you will gain a clear understanding of how to approach problems involving chains, curved surfaces, and acceleration of distributed systems. Such practice is extremely valuable for strengthening your grasp over advanced mechanics and securing a good rank in IIT-JEE Advanced.

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