JEE Main: Centre of Mass of L-Shaped Rod — Smart Method 💡
❓ Question A uniform rod of total length 5L is bent at a right angle , such that one arm has length 2L and the other arm has length 3L . Find the position of the centre of mass of the system. 🖼️ Question Image ✍️ Short Solution This is a standard JEE Centre of Mass problem . No integration needed — treat each arm separately and use weighted average 🔥 🔹 Step 1 — Split the system into two rods Since the rod is uniform : Mass ∝ length Let: Rod 1: length = 2L , along x-axis Rod 2: length = 3L , along y-axis Assume: Total mass = M Mass per unit length = λ \lambda λ Then: Mass of rod 1 = 2 λ L 2\lambda L Mass of rod 2 = 3 λ L 3\lambda L 🔹 Step 2 — Locate centre of mass of each part For a uniform straight rod , COM lies at its midpoint. COM of rod 1 (along x-axis): ( x 1 , y 1 ) = ( L , 0 ) (x_1, y_1) = (L, 0) COM of rod 2 (along y-axis): ( x 2 , y 2 ) = ( 0 , 3 L 2 ) (x_2, y_2) = (0, \tfrac{3L}{2}) 🔹 Step 3 — Use Centre...