Скачать или смотреть The moment of inertia of circular disc of mass ' m ' and radius ' r ' about an axis | PGMN Solutions

The moment of inertia of circular disc of mass ' m ' and radius ' r ' about an axis passing through centre of mass is ' I_0 '. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is
(A) I_0/8
(B) I_0/4
(C) 8I_0
(D) 2I_0



______________________________________________________


🚀 Step-by-Step Solution to Solve This Question 🚀
📌 Chapter: Rotational Dynamics
📌 Topic: Moment of Inertia – Dependence on Mass and Radius

🔹 Step 1: Understand what’s changed
You’re given two discs of same mass and thickness, but the second one has half the density. Moment of inertia depends not only on mass, but also how that mass is distributed — meaning the radius plays a major role.

🔹 Step 2: Think about density and volume
If density is halved and mass is same, then volume must double (since density = mass/volume). With thickness unchanged, the area of the disc must double, and therefore, the radius increases.

🔹 Step 3: Mass stays same, radius increases
Increasing radius (with same mass) means the mass is now spread farther from the axis. Since moment of inertia is highly sensitive to radius, this increases the moment of inertia.

🔹 Step 4: Theoretical conclusion
If the radius increases such that the area becomes twice (due to halved density), then theoretically the new moment of inertia becomes 2 times the original, because the mass is farther from the axis.

✅ Final Answer: (D) 2 I₀ ✅

🔥 Pro Tip: For same mass, when radius increases (due to lower density), moment of inertia increases — even if total mass remains unchanged.


________________________________________________________


📽️ Must watch if you're preparing for MHT-CET 2025 Physics. Perfect for concept clarity & revision.

Welcome to PGMN Solutions – your go-to channel for MHT CET Physics solutions!
🚀 One Question, One Solution – Every Day! 🚀

📌 Get step-by-step solutions to past MHT CET Physics questions, explained by Mukesh Sir.
📌 Master concepts, improve speed, and ace your MHT CET exam with expert guidance.
📌 All solutions are from previous years and important expected questions.

🔔 Subscribe now for daily updates & never miss a solution!
🌐 Visit www.pgmn.live for more Physics resources, test series, and full courses.