Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Concept Question How do we calculate the moment of inertia of a system of different bodies about a given axis? 🖼 Concept Image ✍️ Short Concept MOI depends on: 👉 Mass distribution 👉 Shape of body 👉 Axis of rotation For multiple bodies → calculate individually and then add. 🔷 Step 1 — MOI Depends on Axis 💯 Moment of inertia is not fixed . It depends on: Shape Mass distribution Axis of rotation 👉 Axis change ⇒ MOI change This is the most important idea. 🔷 Step 2 — Different Bodies, Different MOI Even if mass and radius same , formulas differ: Disc → 1 4 M R 2 \frac{1}{4}MR^2  (about diameter) Solid sphere → 2 5 M R 2 \frac{2}{5}MR^2 Spherical shell → 2 3 M R 2 \frac{2}{3}MR^2 📌 JEE mixes these to create confusion. 🔷 Step 3 — Reference MOI Trick Often given: I = MOI of disc about its diameter I = \text{MOI of disc about its diameter} 👉 Convert all other MOIs into multiples of I This simplifies calculati...

  ❓ Question A, B and C are: Disc Solid sphere Spherical shell All have same mass (M) and radius (R) . Moment of inertia of system about PQ axis is: x 15 I \frac{x}{15} I Where: I = MOI of disc about its diameter I = \text{MOI of disc about its diameter} Find x . 🖼 Question Image ✍️ Short Concept This is a standard MOI formula + addition question. Golden idea: 👉 Write MOI of each body about its own center 👉 Convert to required axis (if needed) 👉 Add them 👉 Compare with given I 🔷 Step 1 — Write Standard MOI Formulas 💯 For same mass M and radius R: 🔹 Disc (about diameter) I d = 1 4 M R 2 I_d = \frac{1}{4} MR^2 (This is given as I) 🔹 Solid Sphere (about diameter) I s = 2 5 M R 2 I_s = \frac{2}{5} MR^2 🔹 Spherical Shell (about diameter) I s h = 2 3 M R 2 I_{sh} = \frac{2}{3} MR^2 🔷 Step 2 — Express Everything in Terms of I Given: I = 1 4 M R 2 I = \frac{1}{4} MR^2 So, Solid sphere: 2 5 M R 2 = 2 5 ÷ 1 4   ...