Moment Of Inertia Of A Rod MCQ - Practice Questions & Answers

Solve by difficulty

The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$ . What is the ratio $\frac{l}{R}$ such that the moment of inertia is minimum?

$\sqrt{\frac{3}{2}}$

$\frac{\sqrt{3}}{2}$

$1$

$\frac{3}{\sqrt{2}}$

View Solution

Concepts Covered - 1

Moment of inertia of a Rod

Let I=Moment of inertia of a ROD about an axis through its centre and perpendicular to it

To calculate I (Moment of inertia of rod)

Consider a uniform straight rod of length L, mass M and having centre C

mass per unit length of the rod = $\lambda = \frac{M}{L}$

Take a small element of mass dm with length dx at a distance x from the point C.

$dm = \lambda.dx = \frac{M}{L}.dx$

$\Rightarrow dI= x^2dm$

Now integrate this dI between the limits $x = -\frac{L}{2}\ to \ \frac{L}{2}$

$I=\int dI=\int x^2dm=\int_{\frac{-L}{2}}^{\frac{L}{2}} \frac{M}{L}x^2*dx= \frac{M}{L}\int_{\frac{-L}{2}}^{\frac{L}{2}}x^2dx=\frac{ML^2}{12}$

UPES B.Tech Admissions 2025

Apply

Ranked #42 among Engineering colleges in India by NIRF | Highest CTC 50 LPA , 100% Placements

Integral University B.Tech Admissions 2024

Apply

NAAC A+ Accredited | Highest CTC 12 LPA | Scholarships Available

Parul University B.Tech Admissions 2025

Apply

India's youngest NAAC A++ accredited University | NIRF rank band 151-200 | 2200 Recruiters | 45.98 Lakhs Highest Package

Dayananda Sagar University B.Tech Admissions 2025

Apply

60+ Years of Education Legacy | UGC & AICTE Approved | Prestigious Scholarship Worth 6 Crores | H-CTC 35 LPA

Lovely Professional University B.Tech Admissions 2025

Apply

India's Largest University | NAAC A++ Accredited | 100% Placement Record | Highest Package Offered : 3 Cr PA

Atlas SkillTech University | B.Tech Admissions

Apply

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

Exams

Colleges

Predictors

Resources

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Exams

Predictors & Articles

Colleges

Resources

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Colleges

Resources

Quick Links

Exams

Colleges

Resources

Exams

Colleges

Resources

Diploma Colleges

Exams

Resources

Upcoming Events

Other Exams

Exams

Top Schools

Products & Resources

NCERT Study Material

Exams

Colleges

Top Countries

Student Visas

Exams

Colleges

Upcoming Events

Resources

Engineering Preparation

Medical Preparation

Online Courses

Products

Top Streams

Specializations

Resources

Top Providers

Moment Of Inertia Of A Rod - Practice Questions & MCQ

Quick Facts

Solve by difficulty

Concepts Covered - 1

Study it with Videos

Study other Related Concepts

Moment Of Inertia Of A Rod Current Topic

Get Answer to all your questions

JEE Main Articles

B.Tech/B.Arch Admissions OPEN

UPES B.Tech Admissions 2025

Integral University B.Tech Admissions 2024

Parul University B.Tech Admissions 2025

Dayananda Sagar University B.Tech Admissions 2025

Lovely Professional University B.Tech Admissions 2025

Atlas SkillTech University | B.Tech Admissions

Explore on Careers360

JEE Main