Class 11 Exam > Class 11 Questions > A particle of mass m is projected with a velo...
Start Learning for Free
A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)?
Most Upvoted Answer
A particle of mass m is projected with a velocity v making an angle of...
Solution:
Definition of angular momentum:
Angular momentum is defined as the product of moment of inertia and angular velocity of a body about an axis of rotation.
Equation for angular momentum:
L = Iω
where,
L = Angular momentum
I = Moment of inertia
ω = Angular velocity
Calculation of angular momentum:
At the highest point, the vertical component of velocity becomes zero. So, the projectile moves only in the horizontal direction. Hence, the moment of inertia about the point of projection is given by:
I = mr²
where,
m = Mass of the particle
r = Distance of particle from point of projection
At the highest point, the height of the particle is given by:
h = (v²sin²θ)/2g
where,
θ = Angle of projection
v = Initial velocity of the particle
g = Acceleration due to gravity
Substituting the values in the above equation, we get:
h = (v²/2g)
Therefore, the distance of the particle from the point of projection is given by:
r = h/√2
Substituting the values, we get:
r = v²/2g√2
The angular velocity of the particle is given by:
ω = v/r
Substituting the values, we get:
ω = √2g/v
Therefore, the angular momentum of the particle is given by:
L = Iω = (mr²)(√2g/v)
Substituting the values, we get:
L = (m/2)(v²/2g)(2g/v)
L = mv²/4
Therefore, the magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is mv²/4.
Answer:
Option (B) mv³/4√2g is incorrect. The correct answer is (A) Zero. This is because at the maximum height, the particle has zero vertical velocity, and hence, zero angular momentum about the point of projection.
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 particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)?
Question Description
A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? 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 particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)?.
A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? 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 particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)?.
Solutions for A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? 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 particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? defined & explained in the simplest way possible. Besides giving the explanation of
A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)?, a detailed solution for A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? has been provided alongside types of A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? theory, EduRev gives you an
ample number of questions to practice A particle of mass m is projected with a velocity v making an angle of 45 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is --- A. Zero B. mv³/4√2g C. mv³/√2g D. m√(8gh³)? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup