NEET Exam > NEET Questions > A particle is projected horizontally from the...
Start Learning for Free
A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v?
Most Upvoted Answer
A particle is projected horizontally from the top of a tower with a ve...
Explanation:
When a particle is projected horizontally, it means its initial velocity has no vertical component. Therefore, the particle will only have horizontal motion and its vertical velocity will be zero at all times.
Radius of Curvature:
The radius of curvature represents the curvature of the path of the particle at any instant. It is the radius of the circle that best approximates the shape of the curve at that particular point.
Relationship between Velocity and Radius of Curvature:
The radius of curvature can be related to the velocity of the particle by examining the forces acting on the particle.
The only force acting on the particle in the horizontal direction is the initial velocity, which remains constant throughout the motion. Therefore, the velocity of the particle in the horizontal direction remains constant.
In the vertical direction, the only force acting on the particle is gravity. As a result, the velocity of the particle in the vertical direction increases linearly with time due to the acceleration due to gravity.
Centripetal Force:
As the particle moves horizontally, it experiences a centripetal force towards the center of curvature. This force is provided by the vertical component of the particle's velocity.
The centripetal force is given by the equation: Fc = mv^2 / r, where Fc is the centripetal force, m is the mass of the particle, v is the velocity, and r is the radius of curvature.
Relationship between Radius of Curvature and Velocity:
Using the equation for centripetal force, we can rearrange it to solve for the radius of curvature:
r = mv^2 / Fc
Since the force acting on the particle is the weight (mg) due to gravity, we can substitute Fc with mg:
r = mv^2 / mg
Simplifying the equation, we get:
r = v^2 / g
This equation shows that the radius of curvature is directly proportional to the square of the velocity (v^2) and inversely proportional to the acceleration due to gravity (g).
Answer:
Therefore, the radius of curvature of the path of the particle at any instant is directly proportional to v^2. Hence, the correct option is (b) v^2.
When a particle is projected horizontally, it means its initial velocity has no vertical component. Therefore, the particle will only have horizontal motion and its vertical velocity will be zero at all times.
Radius of Curvature:
The radius of curvature represents the curvature of the path of the particle at any instant. It is the radius of the circle that best approximates the shape of the curve at that particular point.
Relationship between Velocity and Radius of Curvature:
The radius of curvature can be related to the velocity of the particle by examining the forces acting on the particle.
The only force acting on the particle in the horizontal direction is the initial velocity, which remains constant throughout the motion. Therefore, the velocity of the particle in the horizontal direction remains constant.
In the vertical direction, the only force acting on the particle is gravity. As a result, the velocity of the particle in the vertical direction increases linearly with time due to the acceleration due to gravity.
Centripetal Force:
As the particle moves horizontally, it experiences a centripetal force towards the center of curvature. This force is provided by the vertical component of the particle's velocity.
The centripetal force is given by the equation: Fc = mv^2 / r, where Fc is the centripetal force, m is the mass of the particle, v is the velocity, and r is the radius of curvature.
Relationship between Radius of Curvature and Velocity:
Using the equation for centripetal force, we can rearrange it to solve for the radius of curvature:
r = mv^2 / Fc
Since the force acting on the particle is the weight (mg) due to gravity, we can substitute Fc with mg:
r = mv^2 / mg
Simplifying the equation, we get:
r = v^2 / g
This equation shows that the radius of curvature is directly proportional to the square of the velocity (v^2) and inversely proportional to the acceleration due to gravity (g).
Answer:
Therefore, the radius of curvature of the path of the particle at any instant is directly proportional to v^2. Hence, the correct option is (b) v^2.
Community Answer
A particle is projected horizontally from the top of a tower with a ve...
B) v^2
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v?
Question Description
A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v?.
A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v?.
Solutions for A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? defined & explained in the simplest way possible. Besides giving the explanation of
A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v?, a detailed solution for A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? has been provided alongside types of A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? theory, EduRev gives you an
ample number of questions to practice A particle is projected horizontally from the top of a tower with a velocity v0. If v be it's velocity at any instant, then the radius of curvature of the path of the particle at that instant is directly proportional to a) v^3 b) v^2 c) v d) 1/v? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
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