Physics Exam > Physics Questions > Consider a particle of mass mfollowing a traj...
Start Learning for Free
Consider a particle of mass m following a trajectory given by x = x0 cos ω1t and y = y0 sin ω2t,
where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle is
where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle is
- a)central only if ω1 = ω2.
- b)central only if x0 = y0 and ω1 = ω2.
- c)always central.
- d)central only if x0 = y0 and ω1 ≠ ω2.
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Consider a particle of mass mfollowing a trajectory given by x= x0cos ...
Explanation:
To determine whether the force on the particle is central or not, we need to analyze the trajectory and determine if the force depends only on the distance of the particle from a fixed point.
The trajectory of the particle is given by the equations:
x = x0cos(1t)
y = y0sin(2t)
We can see that x depends only on the angle 1t and y depends only on the angle 2t. Therefore, the position of the particle is determined solely by the angles 1t and 2t.
Central Force:
A central force is a force that always acts towards or away from a fixed point, known as the center of force. In other words, the force only depends on the distance of the particle from the fixed point, and not on the direction or angle of the particle.
Analysis:
Let's calculate the velocity and acceleration of the particle to analyze the force acting on it.
Velocity (v):
The velocity of the particle can be obtained by taking the derivatives of x and y with respect to time (t):
v = (dx/dt)i + (dy/dt)j
v = -x0sin(1t)i + 2y0cos(2t)j
Acceleration (a):
Similarly, the acceleration of the particle can be obtained by taking the derivatives of the velocity components with respect to time (t):
a = (dv/dt)i + (dv/dt)j
a = -x0cos(1t)i - 4y0sin(2t)j
Conclusion:
From the analysis of the velocity and acceleration, we can see that the force acting on the particle depends not only on the distance from a fixed point but also on the angles 1t and 2t. Therefore, the force is not central unless 1 = 2. This means that option 'A' is the correct answer.
To determine whether the force on the particle is central or not, we need to analyze the trajectory and determine if the force depends only on the distance of the particle from a fixed point.
The trajectory of the particle is given by the equations:
x = x0cos(1t)
y = y0sin(2t)
We can see that x depends only on the angle 1t and y depends only on the angle 2t. Therefore, the position of the particle is determined solely by the angles 1t and 2t.
Central Force:
A central force is a force that always acts towards or away from a fixed point, known as the center of force. In other words, the force only depends on the distance of the particle from the fixed point, and not on the direction or angle of the particle.
Analysis:
Let's calculate the velocity and acceleration of the particle to analyze the force acting on it.
Velocity (v):
The velocity of the particle can be obtained by taking the derivatives of x and y with respect to time (t):
v = (dx/dt)i + (dy/dt)j
v = -x0sin(1t)i + 2y0cos(2t)j
Acceleration (a):
Similarly, the acceleration of the particle can be obtained by taking the derivatives of the velocity components with respect to time (t):
a = (dv/dt)i + (dv/dt)j
a = -x0cos(1t)i - 4y0sin(2t)j
Conclusion:
From the analysis of the velocity and acceleration, we can see that the force acting on the particle depends not only on the distance from a fixed point but also on the angles 1t and 2t. Therefore, the force is not central unless 1 = 2. This means that option 'A' is the correct answer.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer?
Question Description
Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer?.
Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer?.
Solutions for Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a particle of mass mfollowing a trajectory given by x= x0cos ω1tand y= y0sin ω2t,where x0, y0, ω1, and ω2 are constants of appropriate dimensions. The force on the particle isa)central only if ω1 = ω2.b)central only if x0 = y0 and ω1 = ω2.c)always central.d)central only if x0= y0and ω1 ≠ ω2.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics 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