Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

A circular disc A of radius r is fabricated from an iron plate of...

A circular disc AA of radius rr is fabricated from an iron plate of thickness tt, and a second circular disc BB of radius 4r4r is fabricated from an iron plate of thickness t/4t/4. The relationship between the moments of inertia IAI_A and IBI_B is

Options

  1. AIA<IBI_A < I_B
  2. BIA>IBI_A > I_B
  3. CIA=IBI_A = I_B
  4. Ddepends on the actual values of tt and rr

Correct answer

A. IA<IBI_A < I_B

Step-by-step solution

Let the density of iron be ρ\rho.

The mass of disc A is MA=πr2tρM_A = \pi r^2 t \rho

The moment of inertia of disc A about its central axis is IA=12MAr2=12(πr2tρ)r2=12πρtr4I_A = \dfrac{1}{2} M_A r^2 = \dfrac{1}{2} (\pi r^2 t \rho) r^2 = \dfrac{1}{2} \pi \rho t r^4

The mass of disc B is MB=π(4r)2(t4)ρ=4πr2tρM_B = \pi (4r)^2 \left(\dfrac{t}{4}\right) \rho = 4 \pi r^2 t \rho

The moment of inertia of disc B about its central axis is IB=12MB(4r)2=12(4πr2tρ)(16r2)=32πρtr4I_B = \dfrac{1}{2} M_B (4r)^2 = \dfrac{1}{2} (4 \pi r^2 t \rho) (16r^2) = 32 \pi \rho t r^4

Comparing IAI_A and IBI_B, we get IB=64IAI_B = 64 I_A

Therefore, IA<IBI_A < I_B
Practice Rotational Mechanics on Quantrex Academy →

More from Rotational Mechanics

A wheel revolves about its axis with a uniform angular acceleration. Beginning from rest… Concepts Of Physics MCQ Edition [Volume 1]Starting from rest, a wheel is uniformly accelerated at 4 rad/s^2 for 10 seconds.… Concepts Of Physics MCQ Edition [Volume 1]Determine the angular velocity of a body rotating with an acceleration of 2 rev/s^2 as it… Concepts Of Physics MCQ Edition [Volume 1]A body rotates about a fixed axis with an angular acceleration of one… Concepts Of Physics MCQ Edition [Volume 1]A disc of radius 10 cm rotates about its axis with an angular speed of 20 rad/s .… Concepts Of Physics MCQ Edition [Volume 1]A disc of radius 10 cm rotates about its axis with an angular speed of 20 rad/s .… Concepts Of Physics MCQ Edition [Volume 1]A disc rotates about its axis with a uniform angular acceleration of 4 rad/s^2 .… Concepts Of Physics MCQ Edition [Volume 1]A block is suspended from a string wrapped on a disc of radius 20 cm , which is free to… Concepts Of Physics MCQ Edition [Volume 1] Full Rotational Mechanics list All Concepts Of Physics MCQ Edition [Volume 1] PYQs