JEE Exam > JEE Questions > A particle moves in the xy plane under the ac...
Start Learning for Free
A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will be
- a)180º
- b)90º
- c)30º
- d)0º
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A particle moves in the xy plane under the action of a force F such th...
The angle θ between the direction of the force F and the x-axis can be found using the formula for the dot product of two vectors:
P · F = |P| |F| cos θ
where |P| is the magnitude of the momentum vector P and |F| is the magnitude of the force vector F.
The magnitude of the momentum vector P is given by:
|P| = √(Px^2 + Py^2) = √(4 cos^2 t + 4 sin^2 t) = 2
The time derivative of the momentum vector P is the force vector F:
F = dP/dt = (-2 sin t, 2 cos t)
The magnitude of the force vector F is given by:
|F| = √(Fx^2 + Fy^2) = √(4 sin^2 t + 4 cos^2 t) = 2
Substituting these values into the dot product formula, we get:
2 cos θ = (2)(2) cos θ = Px Fx + Py Fy = 4 cos t (-2 sin t) + 4 sin t (2 cos t) = 0
Simplifying, we get:
-4 sin t cos t + 8 sin t cos t = 0
4 sin t cos t = 0
sin 2t = 0
2t = nπ, where n is an integer
t = nπ/2, where n is an integer
Therefore, the angle θ between the direction of the force F and the x-axis is either 0 or π/2. At t = 0, Px = 2 and Py = 0, so the angle θ is 0. At t = π/2, Px = 0 and Py = 2, so the angle θ is π/2.
P · F = |P| |F| cos θ
where |P| is the magnitude of the momentum vector P and |F| is the magnitude of the force vector F.
The magnitude of the momentum vector P is given by:
|P| = √(Px^2 + Py^2) = √(4 cos^2 t + 4 sin^2 t) = 2
The time derivative of the momentum vector P is the force vector F:
F = dP/dt = (-2 sin t, 2 cos t)
The magnitude of the force vector F is given by:
|F| = √(Fx^2 + Fy^2) = √(4 sin^2 t + 4 cos^2 t) = 2
Substituting these values into the dot product formula, we get:
2 cos θ = (2)(2) cos θ = Px Fx + Py Fy = 4 cos t (-2 sin t) + 4 sin t (2 cos t) = 0
Simplifying, we get:
-4 sin t cos t + 8 sin t cos t = 0
4 sin t cos t = 0
sin 2t = 0
2t = nπ, where n is an integer
t = nπ/2, where n is an integer
Therefore, the angle θ between the direction of the force F and the x-axis is either 0 or π/2. At t = 0, Px = 2 and Py = 0, so the angle θ is 0. At t = π/2, Px = 0 and Py = 2, so the angle θ is π/2.
Free Test
Community Answer
A particle moves in the xy plane under the action of a force F such th...
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer?.
A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A particle moves in the xy plane under the action of a force F such that the value of its linear momentum (P) at any time t is Px=2 cos t, Py=2 sin t. The angle θ between P and F at that time t will bea)180ºb)90ºc)30ºd)0ºCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup