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If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g?
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If trolley accelerated horizontally with acceleration a , then bob is ...
That g cos(theta) component of acceleration of bob is balnced by a sin(theta) component of acceleration of trolley. g sin(theta) and a cos(theta) are in the same direction. Therefore, Net acceleration=g sin(theta) - a cos (theta) Since this is equilibrium condition, a (net) =0 g sin(theta)=a cis(theta) tan (theta)= a/g
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If trolley accelerated horizontally with acceleration a , then bob is ...
Introduction:
In this scenario, we have a trolley that is accelerating horizontally with an acceleration of "a". As a result of this acceleration, a bob suspended vertically from above is displaced backward from its initial vertical position by an angle of 30 degrees. We need to determine the value of "a" in terms of "g", where "g" is the acceleration due to gravity.
Understanding the Problem:
To solve this problem, we need to analyze the forces acting on the bob and understand the relationship between the horizontal acceleration of the trolley and the displacement of the bob.
Forces Acting on the Bob:
1. Weight: The bob experiences a downward force due to gravity, which can be represented by the weight of the bob (mg), where "m" is the mass of the bob and "g" is the acceleration due to gravity.
2. Tension: The bob is suspended from above by a string, which applies an upward force on the bob, known as tension (T).
Analysis:
When the trolley accelerates horizontally, it imparts a horizontal force on the bob due to the tension in the string. This horizontal force causes the bob to displace backward from its initial vertical position.
Components of Forces:
To understand the relationship between the horizontal acceleration of the trolley and the displacement of the bob, we need to consider the components of forces acting on the bob.
1. Vertical Component: The vertical component of the tension force balances the weight of the bob, keeping it in equilibrium.
- T * cos(30°) = mg
2. Horizontal Component: The horizontal component of the tension force causes the bob to accelerate horizontally.
- T * sin(30°) = ma
Solving for "a":
To find the value of "a" in terms of "g", we need to eliminate the tension force (T) in the above equations.
1. Divide the second equation by the first equation:
- (T * sin(30°)) / (T * cos(30°)) = (ma) / (mg)
- tan(30°) = a / g
2. Simplify the equation using the value of tan(30°) (1/√3):
- 1/√3 = a / g
3. Multiply both sides by g:
- g/√3 = a
Conclusion:
The value of "a" in terms of "g" is g/√3. The horizontal acceleration of the trolley is equal to the acceleration due to gravity divided by the square root of 3.
In this scenario, we have a trolley that is accelerating horizontally with an acceleration of "a". As a result of this acceleration, a bob suspended vertically from above is displaced backward from its initial vertical position by an angle of 30 degrees. We need to determine the value of "a" in terms of "g", where "g" is the acceleration due to gravity.
Understanding the Problem:
To solve this problem, we need to analyze the forces acting on the bob and understand the relationship between the horizontal acceleration of the trolley and the displacement of the bob.
Forces Acting on the Bob:
1. Weight: The bob experiences a downward force due to gravity, which can be represented by the weight of the bob (mg), where "m" is the mass of the bob and "g" is the acceleration due to gravity.
2. Tension: The bob is suspended from above by a string, which applies an upward force on the bob, known as tension (T).
Analysis:
When the trolley accelerates horizontally, it imparts a horizontal force on the bob due to the tension in the string. This horizontal force causes the bob to displace backward from its initial vertical position.
Components of Forces:
To understand the relationship between the horizontal acceleration of the trolley and the displacement of the bob, we need to consider the components of forces acting on the bob.
1. Vertical Component: The vertical component of the tension force balances the weight of the bob, keeping it in equilibrium.
- T * cos(30°) = mg
2. Horizontal Component: The horizontal component of the tension force causes the bob to accelerate horizontally.
- T * sin(30°) = ma
Solving for "a":
To find the value of "a" in terms of "g", we need to eliminate the tension force (T) in the above equations.
1. Divide the second equation by the first equation:
- (T * sin(30°)) / (T * cos(30°)) = (ma) / (mg)
- tan(30°) = a / g
2. Simplify the equation using the value of tan(30°) (1/√3):
- 1/√3 = a / g
3. Multiply both sides by g:
- g/√3 = a
Conclusion:
The value of "a" in terms of "g" is g/√3. The horizontal acceleration of the trolley is equal to the acceleration due to gravity divided by the square root of 3.
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If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g?
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If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g?.
If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If trolley accelerated horizontally with acceleration a , then bob is displaced backward from its initial vertical position by an angle 30 degree. What is the value of a in terms of g?.
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