JEE Exam > JEE Questions > A simple pendulum made of a bob of mass m and...
Start Learning for Free
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :
- a)α
- b)α/2
- c)2α
- d)1/α
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A simple pendulum made of a bob of mass m and a metallic wire of negli...
Assuming that the pendulum is undergoing small oscillations, we can use the formula for the time period of a simple pendulum:
T = 2π√(l/g)
where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.
At T=0, we know that the time period is 2 seconds. Therefore, we can write:
2 = 2π√(l/g)
Squaring both sides, we get:
4 = 4π^2(l/g)
Dividing both sides by 4π^2, we get:
l/g = 1/π^2
Rearranging, we get:
l = g/π^2
Now, we can use this value of l to find the length of the pendulum required for a time period of 1 second:
1 = 2π√(l/g)
Squaring both sides and substituting the value of l, we get:
1 = 4π^2(g/π^2)/g
Simplifying, we get:
1 = 4π^2/π^2
Therefore, the length of the pendulum required for a time period of 1 second is:
l = g/π^2 = 9.81/π^2 meters
Note that this calculation assumes that the amplitude of the oscillations is small enough that the pendulum can be considered a simple harmonic oscillator. If the amplitude is too large, the pendulum's motion may become nonlinear and the time period may be different than what is predicted by this formula.
T = 2π√(l/g)
where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.
At T=0, we know that the time period is 2 seconds. Therefore, we can write:
2 = 2π√(l/g)
Squaring both sides, we get:
4 = 4π^2(l/g)
Dividing both sides by 4π^2, we get:
l/g = 1/π^2
Rearranging, we get:
l = g/π^2
Now, we can use this value of l to find the length of the pendulum required for a time period of 1 second:
1 = 2π√(l/g)
Squaring both sides and substituting the value of l, we get:
1 = 4π^2(g/π^2)/g
Simplifying, we get:
1 = 4π^2/π^2
Therefore, the length of the pendulum required for a time period of 1 second is:
l = g/π^2 = 9.81/π^2 meters
Note that this calculation assumes that the amplitude of the oscillations is small enough that the pendulum can be considered a simple harmonic oscillator. If the amplitude is too large, the pendulum's motion may become nonlinear and the time period may be different than what is predicted by this formula.
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
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer?
Question Description
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer?.
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? 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 A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T=0ºC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is α then the value of S is :a)αb)α/2c)2αd)1/αCorrect answer is option 'B'. Can you explain this answer? 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup