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It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct?
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It's given that, T stands for time period; L stands for length; of a s...
The relation T^2 = l/g is dimensionally correct. The thing that you might be confusing is that "All correct physically plausible relations must always be dimensionally correct but all dimensionally correct relations need not be the exact physical relation between two physical quantities." It should be determined experimentally, or if enough physical laws are known, should be deduced based on it.Further, as an example v^2 = u ^2 + a*s , where v, u, a and s are respectively velocity, initial velocity, acceleration and displacement is a dimensionally correct relation but not the exact relationship between these variables.
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It's given that, T stands for time period; L stands for length; of a s...
Relation between Time Period and Length of a Simple Pendulum
Understanding the Relationship
- The time period (T) of a simple pendulum is the time taken for one complete oscillation.
- The length (L) of the pendulum and the acceleration due to gravity (g) are two key factors that affect the time period.
Mathematical Relation
- The formula for the time period of a simple pendulum is given by T = 2π√(L/g).
- Squaring both sides of the equation gives T^2 = 4π^2(L/g).
Verification of the Relation T^2 = (1/g)
- If we substitute T^2 = 4π^2(L/g) into T^2 = (1/g), we get 4π^2(L/g) = (1/g).
- By simplifying the equation, we get 4π^2L = 1.
- Since there is no g on the left-hand side of the equation, it is evident that the relation T^2 = (1/g) is incorrect.
Conclusion
- The correct relation between the time period and acceleration due to gravity is T^2 = 4π^2(L/g), as derived from the formula for the time period of a simple pendulum. It is essential to use the accurate formula to calculate the time period correctly in physics experiments involving pendulums.
Understanding the Relationship
- The time period (T) of a simple pendulum is the time taken for one complete oscillation.
- The length (L) of the pendulum and the acceleration due to gravity (g) are two key factors that affect the time period.
Mathematical Relation
- The formula for the time period of a simple pendulum is given by T = 2π√(L/g).
- Squaring both sides of the equation gives T^2 = 4π^2(L/g).
Verification of the Relation T^2 = (1/g)
- If we substitute T^2 = 4π^2(L/g) into T^2 = (1/g), we get 4π^2(L/g) = (1/g).
- By simplifying the equation, we get 4π^2L = 1.
- Since there is no g on the left-hand side of the equation, it is evident that the relation T^2 = (1/g) is incorrect.
Conclusion
- The correct relation between the time period and acceleration due to gravity is T^2 = 4π^2(L/g), as derived from the formula for the time period of a simple pendulum. It is essential to use the accurate formula to calculate the time period correctly in physics experiments involving pendulums.
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It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct?
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It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct?.
It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It's given that, T stands for time period; L stands for length; of a simple pendulum. If "g" is the acceleration due to gravity, then is the relation "T^2 = (1/g) correct?.
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