JEE Exam > JEE Questions > Thin uniform bar of mass m and length 2L is h...
Start Learning for Free
Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break?
Most Upvoted Answer
Thin uniform bar of mass m and length 2L is held at an angle son with ...
Analysis:
The given problem involves the application of Newton's laws of motion and torque to determine the tension in the string at the left end and the angular acceleration of the bar after the right string breaks.
Free Body Diagram:
- Draw a free body diagram of the bar showing all the forces acting on it.
- The forces acting on the bar are tension T at the left end, tension T' at the right end, weight mg acting at the center of the bar, and the reaction force R at the pivot point.
Equations of Motion:
- Apply Newton's second law in the vertical direction to determine the tension T.
- Apply the torque equation about the pivot point to determine the angular acceleration of the bar.
Equation for Tension:
- Resolving forces vertically, we get T - mgcosθ = 0, where θ is the angle of inclination.
- Solving for T, we get T = mgcosθ.
Equation for Angular Acceleration:
- Taking the torque about the pivot point, we get T' * 2L = I * α, where I is the moment of inertia of the bar about the pivot point and α is the angular acceleration.
- Substituting the values and solving, we get α = 3g / (2L).
Therefore, the tension in the string at the left end is T = mgcosθ and the angular acceleration of the bar immediately after the string break is α = 3g / (2L).
The given problem involves the application of Newton's laws of motion and torque to determine the tension in the string at the left end and the angular acceleration of the bar after the right string breaks.
Free Body Diagram:
- Draw a free body diagram of the bar showing all the forces acting on it.
- The forces acting on the bar are tension T at the left end, tension T' at the right end, weight mg acting at the center of the bar, and the reaction force R at the pivot point.
Equations of Motion:
- Apply Newton's second law in the vertical direction to determine the tension T.
- Apply the torque equation about the pivot point to determine the angular acceleration of the bar.
Equation for Tension:
- Resolving forces vertically, we get T - mgcosθ = 0, where θ is the angle of inclination.
- Solving for T, we get T = mgcosθ.
Equation for Angular Acceleration:
- Taking the torque about the pivot point, we get T' * 2L = I * α, where I is the moment of inertia of the bar about the pivot point and α is the angular acceleration.
- Substituting the values and solving, we get α = 3g / (2L).
Therefore, the tension in the string at the left end is T = mgcosθ and the angular acceleration of the bar immediately after the string break is α = 3g / (2L).
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break?
Question Description
Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break?.
Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break?.
Solutions for Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? defined & explained in the simplest way possible. Besides giving the explanation of
Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break?, a detailed solution for Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? has been provided alongside types of Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? theory, EduRev gives you an
ample number of questions to practice Thin uniform bar of mass m and length 2L is held at an angle son with the horizontal by means of two vertical inextensible strings, at each end as shown in figure. If the string at the right end breaks, leaving the bar to swing, determine the tension in the string at the left end and the angular acceleration of the bar immediately after string break? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup