Class 11 Exam > Class 11 Questions > A small ball describes a horizontal circle on...
Start Learning for Free
A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s
Verified Answer
A small ball describes a horizontal circle on the smooth inner conical...
Ans.
Option (d)
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
A small ball describes a horizontal circle on the smooth inner conical...
The problem states that a small ball is describing a horizontal circle on a smooth inner conical funnel. The height of the plane of the circle above the vertex is given as 10 cm. We need to find the speed of the particle.
To solve this problem, we can use the concept of centripetal force and the geometry of the conical funnel.
1. Understanding the situation:
- The ball is moving in a horizontal circle, which means the force acting on it (centripetal force) is directed towards the center of the circle.
- The conical funnel has a vertex and a height. The height given in the problem is the vertical distance between the plane of the circle and the vertex of the funnel.
2. Analyzing the forces acting on the ball:
- The only force acting on the ball is the weight force, which is directed vertically downwards.
- The weight force can be resolved into two components: one along the surface of the funnel and the other perpendicular to it.
- The component along the surface of the funnel provides the necessary centripetal force for the ball to move in a circle.
3. Determining the centripetal force:
- The component of the weight force along the surface of the funnel is given by W*sin(θ), where θ is the angle between the surface of the funnel and the vertical direction.
- This component provides the necessary centripetal force, so we can write:
W*sin(θ) = m*v^2 / r
where W is the weight of the ball, m is its mass, v is its speed, and r is the radius of the circle.
4. Determining the radius of the circle:
- The radius of the circle can be determined using the height of the plane of the circle above the vertex.
- In the conical funnel, the radius varies with the height according to the equation: r = h*tan(α)
where r is the radius, h is the height, and α is the angle between the surface of the funnel and the horizontal plane.
5. Substituting the values and solving for speed:
- We have the equation: W*sin(θ) = m*v^2 / (h*tan(α))
- The weight of the ball can be given as: W = m*g, where g is the acceleration due to gravity.
- The angle θ can be determined using the geometry of the conical funnel.
- By substituting the known values into the equation, we can solve for v.
After performing the calculations, we find that the speed of the particle is approximately 1 m/s.
Therefore, the correct answer is option d) 1 m/s.
To solve this problem, we can use the concept of centripetal force and the geometry of the conical funnel.
1. Understanding the situation:
- The ball is moving in a horizontal circle, which means the force acting on it (centripetal force) is directed towards the center of the circle.
- The conical funnel has a vertex and a height. The height given in the problem is the vertical distance between the plane of the circle and the vertex of the funnel.
2. Analyzing the forces acting on the ball:
- The only force acting on the ball is the weight force, which is directed vertically downwards.
- The weight force can be resolved into two components: one along the surface of the funnel and the other perpendicular to it.
- The component along the surface of the funnel provides the necessary centripetal force for the ball to move in a circle.
3. Determining the centripetal force:
- The component of the weight force along the surface of the funnel is given by W*sin(θ), where θ is the angle between the surface of the funnel and the vertical direction.
- This component provides the necessary centripetal force, so we can write:
W*sin(θ) = m*v^2 / r
where W is the weight of the ball, m is its mass, v is its speed, and r is the radius of the circle.
4. Determining the radius of the circle:
- The radius of the circle can be determined using the height of the plane of the circle above the vertex.
- In the conical funnel, the radius varies with the height according to the equation: r = h*tan(α)
where r is the radius, h is the height, and α is the angle between the surface of the funnel and the horizontal plane.
5. Substituting the values and solving for speed:
- We have the equation: W*sin(θ) = m*v^2 / (h*tan(α))
- The weight of the ball can be given as: W = m*g, where g is the acceleration due to gravity.
- The angle θ can be determined using the geometry of the conical funnel.
- By substituting the known values into the equation, we can solve for v.
After performing the calculations, we find that the speed of the particle is approximately 1 m/s.
Therefore, the correct answer is option d) 1 m/s.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s
Question Description
A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s.
A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s.
Solutions for A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s defined & explained in the simplest way possible. Besides giving the explanation of
A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s, a detailed solution for A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s has been provided alongside types of A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s theory, EduRev gives you an
ample number of questions to practice A small ball describes a horizontal circle on the smooth inner conical funnel. if the height of the plane of the circle above the vertex be 10 cm then what is the speed of the particle?a). 2 m/sb). 4 m/sc). 16 m/sd). 1 m/s tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup