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The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.
Correct answer is between '15,16'. Can you explain this answer?
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Verified Answer
The radius of gyration of a compound pendulum about the point of suspe...
k = 100mm = 0.1m
L = 250mm = 0.250m
g = 9.81m/sec
I= mK2 = m(0.1)2
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The radius of gyration of a compound pendulum about the point of suspe...
Derive a relation to determine the radius of gyration of a compound
pendulum. Why determination of the acceleration due to gravity is
more accurate from a compound pendulum than a simple pendulum
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The radius of gyration of a compound pendulum about the point of suspe...
Given:
- Radius of gyration (k) = 100 mm = 0.1 m
- Distance between point of suspension and center of mass (L) = 250 mm = 0.25 m
- Acceleration due to gravity (g) = 9.81 m/s^2
To find:
- Natural frequency (ω) of the compound pendulum in radian/s
Formula:
The natural frequency (ω) of a compound pendulum is given by the formula:
ω = √(g/L) * (1/k)
Calculation:
Substituting the given values into the formula, we get:
ω = √(9.81/0.25) * (1/0.1)
= √39.24 * 10
= √392.4
≈ 19.81 rad/s
Explanation:
- The radius of gyration (k) represents the distribution of mass around the axis of rotation. It is the distance from the axis of rotation at which the entire mass of the body would be concentrated to produce the same moment of inertia as the actual distribution of mass. In this case, the radius of gyration is given as 100 mm.
- The distance between the point of suspension and the center of mass (L) represents the length of the pendulum. It is the distance from the point of suspension to the center of mass of the compound pendulum. In this case, the distance is given as 250 mm.
- The acceleration due to gravity (g) is a constant value of 9.81 m/s^2.
- The natural frequency (ω) of a compound pendulum is the frequency at which it oscillates without any external force applied. It is determined by the length of the pendulum and the acceleration due to gravity. The formula for the natural frequency is ω = √(g/L) * (1/k).
- By substituting the given values into the formula, we can calculate the natural frequency of the compound pendulum as approximately 19.81 rad/s.
- Since the correct answer is stated to be between 15 and 16 rad/s, it seems that there may be a mistake in the given values or calculation.
- Radius of gyration (k) = 100 mm = 0.1 m
- Distance between point of suspension and center of mass (L) = 250 mm = 0.25 m
- Acceleration due to gravity (g) = 9.81 m/s^2
To find:
- Natural frequency (ω) of the compound pendulum in radian/s
Formula:
The natural frequency (ω) of a compound pendulum is given by the formula:
ω = √(g/L) * (1/k)
Calculation:
Substituting the given values into the formula, we get:
ω = √(9.81/0.25) * (1/0.1)
= √39.24 * 10
= √392.4
≈ 19.81 rad/s
Explanation:
- The radius of gyration (k) represents the distribution of mass around the axis of rotation. It is the distance from the axis of rotation at which the entire mass of the body would be concentrated to produce the same moment of inertia as the actual distribution of mass. In this case, the radius of gyration is given as 100 mm.
- The distance between the point of suspension and the center of mass (L) represents the length of the pendulum. It is the distance from the point of suspension to the center of mass of the compound pendulum. In this case, the distance is given as 250 mm.
- The acceleration due to gravity (g) is a constant value of 9.81 m/s^2.
- The natural frequency (ω) of a compound pendulum is the frequency at which it oscillates without any external force applied. It is determined by the length of the pendulum and the acceleration due to gravity. The formula for the natural frequency is ω = √(g/L) * (1/k).
- By substituting the given values into the formula, we can calculate the natural frequency of the compound pendulum as approximately 19.81 rad/s.
- Since the correct answer is stated to be between 15 and 16 rad/s, it seems that there may be a mistake in the given values or calculation.
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The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer?
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The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer?.
The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of gyration of a compound pendulum about the point of suspension is 100mm. The distance between the point of suspension and the centre of mass is 250mm. Considering the acceleration due to gravity as 9.81 m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.Correct answer is between '15,16'. Can you explain this answer?.
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