GATE Exam  >  GATE Questions  >  A centiliver beam of negligible mass 0.6m .it... Start Learning for Free
A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material?
Most Upvoted Answer
A centiliver beam of negligible mass 0.6m .it has rectangular cross-se...
Calculation of Young's modulus of a Centiliver beam


Given


  • Length of the beam, L = 0.6m

  • Width of the beam, b = 8mm = 0.008m

  • Height of the beam, h = 6mm = 0.006m

  • Mass of the beam, m = 1.4kg

  • Natural frequency of the system, f = 10 rad/s



Formula

The natural frequency of a beam is given by:

f = (1/2π) √(EI/ml^3)

where E is the Young's modulus of the material, I is the moment of inertia of the cross-section of the beam, and m is the mass of the beam.

The moment of inertia of a rectangular cross-section is given by:

I = bh^3/12

Young's modulus is given by:

E = (mL^3f^2)/(4b^3h^3π^2)

Solution

Substituting the given values in the formula:

I = (0.008 x 0.006^3)/12 = 8 x 10^-11 m^4

E = (1.4 x 0.6^3 x 10^2)/(4 x 0.008^3 x 0.006^3 x π^2) = 1.2 x 10^11 Pa


Therefore, the Young's modulus of the material of the beam is 1.2 x 10^11 Pa.

Explanation

A Centiliver beam is a type of beam that is clamped at one end and free at the other end. The natural frequency of such a beam depends on the length, mass, and Young's modulus of the material. The formula for calculating the natural frequency involves the moment of inertia of the cross-section, which depends on the width and height of the beam. The Young's modulus is a measure of the stiffness of the material and is given by the ratio of stress to strain. In this problem, we use the formula for the natural frequency of a beam and the moment of inertia of a rectangular cross-section to calculate the Young's modulus of the material of the beam.
Explore Courses for GATE exam
A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material?
Question Description
A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material?.
Solutions for A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? defined & explained in the simplest way possible. Besides giving the explanation of A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material?, a detailed solution for A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? has been provided alongside types of A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? theory, EduRev gives you an ample number of questions to practice A centiliver beam of negligible mass 0.6m .it has rectangular cross-section of width 8mm and hight 6mm kept mass 1.4kg .if natural frequency is this system 10rad/sb.the Young's modulus of material? tests, examples and also practice GATE tests.
Explore Courses for GATE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev