Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

🌀 Centroid of a Circular Plate with a Hole | System of Particles | JEE Physics | Doubtify JEE ❓ Question: A circular hole of radius (a/2) is cut out of a circular disc of radius ‘a’ , as shown in the figure. What will be the position of the centroid of the remaining circular portion with respect to point ‘O’ ? 🖼️ Question Image: 🧠 Solution Image: ✍️ Detailed Explanation: To solve this problem, we apply the concept of mass moment (or area moment) . When a portion is cut out from a symmetric object, we use the principle of superposition — treat the hole as a negative mass or negative area. Let’s break it down: 🧮 Step 1: Assume mass per unit area = σ Area of full disc = πa² Area of hole = π(a/2)² = (πa²)/4 Remaining area = πa² – (πa²)/4 = (3πa²)/4 🧮 Step 2: Find centroid of each part Full disc’s centroid = At origin (O) Hole’s centroid is at a distance of a/2 from O along the radius. 🧮 Step 3: Apply formula for center of mass (COM): Let x be the position of the c...