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If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will be
- a)decreased by 4-fold.
- b)increased by 4-fold.
- c)decreased to half of the initial value.
- d)increased by a factor of 2 of its initial value.
Correct answer is option 'D'. Can you explain this answer?
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Pendulum and Time Period
A simple pendulum consists of a mass (bob) attached to a string or rod of a certain length. When the pendulum is displaced from its equilibrium position and released, it oscillates back and forth under the influence of gravity. The time taken for one complete oscillation is called the time period of the pendulum.
Effect of Length on Time Period
The time period of a simple pendulum is directly proportional to the square root of its length. Mathematically, the time period (T) is given by the formula:
T = 2π√(L/g)
Where:
T = time period
L = length of the pendulum
g = acceleration due to gravity
Effect of Increasing Length
When the length of a simple pendulum is increased by 4-fold, the new length becomes 4L. Let's analyze the effect of this change on the time period.
Using the formula mentioned earlier, we can write the new time period (T') as:
T' = 2π√(4L/g)
Simplifying this equation, we get:
T' = 2π√(4)√(L/g)
= 2π(2)√(L/g)
= 4π√(L/g)
Comparison of Time Periods
Now, let's compare the new time period (T') with the initial time period (T).
T' = 4π√(L/g)
T = 2π√(L/g)
We can observe that T' is equal to 2 times T. Therefore, the time period of oscillation is increased by a factor of 2 when the length of the pendulum is increased by 4-fold.
Conclusion
In conclusion, when the length of a simple pendulum is increased by 4-fold, the time period of oscillation is increased by a factor of 2 of its initial value. Thus, the correct answer is option 'D'.
A simple pendulum consists of a mass (bob) attached to a string or rod of a certain length. When the pendulum is displaced from its equilibrium position and released, it oscillates back and forth under the influence of gravity. The time taken for one complete oscillation is called the time period of the pendulum.
Effect of Length on Time Period
The time period of a simple pendulum is directly proportional to the square root of its length. Mathematically, the time period (T) is given by the formula:
T = 2π√(L/g)
Where:
T = time period
L = length of the pendulum
g = acceleration due to gravity
Effect of Increasing Length
When the length of a simple pendulum is increased by 4-fold, the new length becomes 4L. Let's analyze the effect of this change on the time period.
Using the formula mentioned earlier, we can write the new time period (T') as:
T' = 2π√(4L/g)
Simplifying this equation, we get:
T' = 2π√(4)√(L/g)
= 2π(2)√(L/g)
= 4π√(L/g)
Comparison of Time Periods
Now, let's compare the new time period (T') with the initial time period (T).
T' = 4π√(L/g)
T = 2π√(L/g)
We can observe that T' is equal to 2 times T. Therefore, the time period of oscillation is increased by a factor of 2 when the length of the pendulum is increased by 4-fold.
Conclusion
In conclusion, when the length of a simple pendulum is increased by 4-fold, the time period of oscillation is increased by a factor of 2 of its initial value. Thus, the correct answer is option 'D'.
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If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer?
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If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer?.
If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of a simple pendulum is being increased by 4-fold, time period of oscillation will bea)decreased by 4-fold.b)increased by 4-fold.c)decreased to half of the initial value.d)increased by a factor of 2 of its initial value.Correct answer is option 'D'. Can you explain this answer?.
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