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A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be?
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A mass m on a frictionless table is attached by a hanging mass with sp...
Ans.
Method to Solve :
Let x= increase in lenght of string
Then the particle moves along the circular path.of radius (l+x)
and the spring force =kx=centripatal force
This question is part of UPSC exam. View all JEE courses
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A mass m on a frictionless table is attached by a hanging mass with sp...
Problem Statement:
A mass m is attached to a hanging mass with a spring of spring constant K and natural length l. The hanging mass remains stationary while the mass m moves in a circular path with a constant angular speed "w". We need to find the radius of the circular path.
Solution:
1. Free Body Diagram:
To analyze the system, let's start by drawing a free body diagram of the mass m. The forces acting on the mass m are:
- Tension force T in the cord
- Centripetal force Fc
2. Tension Force:
The tension force T in the cord can be determined by balancing the forces in the vertical direction. Since the hanging mass remains stationary, the tension force T is equal to the weight of the hanging mass:
T = m * g, where g is the acceleration due to gravity.
3. Centripetal Force:
The centripetal force Fc is required to keep the mass m moving in a circular path. It can be calculated using the formula:
Fc = m * (w^2) * r, where m is the mass of the moving object, w is the angular speed, and r is the radius of the circular path.
4. Equating Forces:
Since the hanging mass remains stationary, the tension force T is equal to the centripetal force Fc:
m * g = m * (w^2) * r
5. Solving for Radius:
We can rearrange the equation to solve for the radius r:
r = (m * g) / (m * (w^2))
r = g / (w^2)
Conclusion:
The radius of the circular path on which the mass m moves with a constant angular speed "w" is given by the formula r = g / (w^2). The value of the radius depends on the acceleration due to gravity (g) and the square of the angular speed (w^2).
A mass m is attached to a hanging mass with a spring of spring constant K and natural length l. The hanging mass remains stationary while the mass m moves in a circular path with a constant angular speed "w". We need to find the radius of the circular path.
Solution:
1. Free Body Diagram:
To analyze the system, let's start by drawing a free body diagram of the mass m. The forces acting on the mass m are:
- Tension force T in the cord
- Centripetal force Fc
2. Tension Force:
The tension force T in the cord can be determined by balancing the forces in the vertical direction. Since the hanging mass remains stationary, the tension force T is equal to the weight of the hanging mass:
T = m * g, where g is the acceleration due to gravity.
3. Centripetal Force:
The centripetal force Fc is required to keep the mass m moving in a circular path. It can be calculated using the formula:
Fc = m * (w^2) * r, where m is the mass of the moving object, w is the angular speed, and r is the radius of the circular path.
4. Equating Forces:
Since the hanging mass remains stationary, the tension force T is equal to the centripetal force Fc:
m * g = m * (w^2) * r
5. Solving for Radius:
We can rearrange the equation to solve for the radius r:
r = (m * g) / (m * (w^2))
r = g / (w^2)
Conclusion:
The radius of the circular path on which the mass m moves with a constant angular speed "w" is given by the formula r = g / (w^2). The value of the radius depends on the acceleration due to gravity (g) and the square of the angular speed (w^2).
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A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be?
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A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be?.
A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mass m on a frictionless table is attached by a hanging mass with spring of spring constant K having natural length l and a cord through a hole in a table , if hanging mass remains stationary and mass m moves in a circular with a constant angular speed "w" the radius of the circular path will be?.
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