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Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ?
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Consider a simple pendulum of length 1 m its bob performs a circular m...
Introduction:
In this problem, we are given a simple pendulum of length 1 m with its bob making an angle of 60 degrees with the vertical. We need to find the centripetal acceleration experienced by the bob.
Formula:
The centripetal acceleration of an object moving in a circular path is given by the formula:
a = v^2/r
where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.
Analysis:
In this problem, the bob of the pendulum is moving in a circular path with a radius of 1 m. We need to find the velocity of the bob in order to calculate the centripetal acceleration.
Solution:
To find the velocity of the bob, we need to use the formula for the period of a pendulum:
T = 2π√(l/g)
where T is the period of the pendulum, l is the length of the pendulum, and g is the acceleration due to gravity.
Substituting the given values, we get:
T = 2π√(1/9.81)
T = 2.006 s
The velocity of the bob can be found using the formula:
v = 2πr/T
where v is the velocity of the bob and r is the radius of the circular path.
Substituting the given values, we get:
v = 2π(1)/2.006
v = 3.135 m/s
Now, using the formula for centripetal acceleration, we get:
a = v^2/r
a = (3.135)^2/1
a = 9.82 m/s^2
Conclusion:
Therefore, the centripetal acceleration experienced by the bob of the pendulum is 9.82 m/s^2.
In this problem, we are given a simple pendulum of length 1 m with its bob making an angle of 60 degrees with the vertical. We need to find the centripetal acceleration experienced by the bob.
Formula:
The centripetal acceleration of an object moving in a circular path is given by the formula:
a = v^2/r
where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the circular path.
Analysis:
In this problem, the bob of the pendulum is moving in a circular path with a radius of 1 m. We need to find the velocity of the bob in order to calculate the centripetal acceleration.
Solution:
To find the velocity of the bob, we need to use the formula for the period of a pendulum:
T = 2π√(l/g)
where T is the period of the pendulum, l is the length of the pendulum, and g is the acceleration due to gravity.
Substituting the given values, we get:
T = 2π√(1/9.81)
T = 2.006 s
The velocity of the bob can be found using the formula:
v = 2πr/T
where v is the velocity of the bob and r is the radius of the circular path.
Substituting the given values, we get:
v = 2π(1)/2.006
v = 3.135 m/s
Now, using the formula for centripetal acceleration, we get:
a = v^2/r
a = (3.135)^2/1
a = 9.82 m/s^2
Conclusion:
Therefore, the centripetal acceleration experienced by the bob of the pendulum is 9.82 m/s^2.
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Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ?
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Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ?.
Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a simple pendulum of length 1 m its bob performs a circular motion in horizontal plane with its string making an angle 60 degrees with the vertical find the centripetal acceleration experienced by the bob ?.
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