GATE Exam > GATE Questions > A system of four particles is in x-y plane of...
Start Learning for Free
A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle is
- a)10m
- b)-10m
- c)0m
- d)-2m
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A system of four particles is in x-y plane of these two particle of ma...
The xy component of inertia tensor is
Ixy = -[(m x1x1) + (m x-1x1) + (2m x1x-1) + 2m(-1x-1)]
= - [ m - m - 2m + 2m ]
= 0
Ixy = -[(m x1x1) + (m x-1x1) + (2m x1x-1) + 2m(-1x-1)]
= - [ m - m - 2m + 2m ]
= 0
Most Upvoted Answer
A system of four particles is in x-y plane of these two particle of ma...
To find the xy component of the moment of inertia tensor of the system of particles, we need to calculate the moment of inertia of each particle about the xy plane and then sum them up.
1. Moment of Inertia of Particle 1 (m1):
The moment of inertia of Particle 1 about the xy plane is given by: I1 = m1 * r1^2, where r1 is the perpendicular distance of the particle from the xy plane. In this case, r1 = 1 (since the particle is located at (1, 1)).
Therefore, I1 = m * 1^2 = m.
2. Moment of Inertia of Particle 2 (m2):
The moment of inertia of Particle 2 about the xy plane is given by: I2 = m2 * r2^2, where r2 is the perpendicular distance of the particle from the xy plane. In this case, r2 = 1 (since the particle is located at (-1, 1)).
Therefore, I2 = m * 1^2 = m.
3. Moment of Inertia of Particle 3 (m3):
The moment of inertia of Particle 3 about the xy plane is given by: I3 = m3 * r3^2, where r3 is the perpendicular distance of the particle from the xy plane. In this case, r3 = 1 (since the particle is located at (1, -1)).
Therefore, I3 = 2m * 1^2 = 2m.
4. Moment of Inertia of Particle 4 (m4):
The moment of inertia of Particle 4 about the xy plane is given by: I4 = m4 * r4^2, where r4 is the perpendicular distance of the particle from the xy plane. In this case, r4 = 1 (since the particle is located at (-1, -1)).
Therefore, I4 = 2m * 1^2 = 2m.
5. Summing up the Moments of Inertia:
Now, we can sum up the moments of inertia of all the particles to get the moment of inertia of the system of particles about the xy plane.
Ixy = I1 + I2 + I3 + I4
= m + m + 2m + 2m
= 6m.
Therefore, the xy component of the moment of inertia tensor of the system of particles is 6m. However, the given options do not have 6m as a choice. So, it seems that there might be an error in the options provided.
In conclusion, the correct answer cannot be determined from the given options.
1. Moment of Inertia of Particle 1 (m1):
The moment of inertia of Particle 1 about the xy plane is given by: I1 = m1 * r1^2, where r1 is the perpendicular distance of the particle from the xy plane. In this case, r1 = 1 (since the particle is located at (1, 1)).
Therefore, I1 = m * 1^2 = m.
2. Moment of Inertia of Particle 2 (m2):
The moment of inertia of Particle 2 about the xy plane is given by: I2 = m2 * r2^2, where r2 is the perpendicular distance of the particle from the xy plane. In this case, r2 = 1 (since the particle is located at (-1, 1)).
Therefore, I2 = m * 1^2 = m.
3. Moment of Inertia of Particle 3 (m3):
The moment of inertia of Particle 3 about the xy plane is given by: I3 = m3 * r3^2, where r3 is the perpendicular distance of the particle from the xy plane. In this case, r3 = 1 (since the particle is located at (1, -1)).
Therefore, I3 = 2m * 1^2 = 2m.
4. Moment of Inertia of Particle 4 (m4):
The moment of inertia of Particle 4 about the xy plane is given by: I4 = m4 * r4^2, where r4 is the perpendicular distance of the particle from the xy plane. In this case, r4 = 1 (since the particle is located at (-1, -1)).
Therefore, I4 = 2m * 1^2 = 2m.
5. Summing up the Moments of Inertia:
Now, we can sum up the moments of inertia of all the particles to get the moment of inertia of the system of particles about the xy plane.
Ixy = I1 + I2 + I3 + I4
= m + m + 2m + 2m
= 6m.
Therefore, the xy component of the moment of inertia tensor of the system of particles is 6m. However, the given options do not have 6m as a choice. So, it seems that there might be an error in the options provided.
In conclusion, the correct answer cannot be determined from the given options.
|
Explore Courses for GATE exam
|
|
A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer?
Question Description
A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer?.
A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A system of four particles is in x-y plane of these two particle of masses m are located at (1,1) and (-1,1). The remaining two particles each of mass 2m are located at (1,-1) and (-1,-1). The xy component of moment of inertia tensor of the system of particle isa)10mb)-10mc)0md)-2mCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE 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