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Magnetic moments of two identical magnets are M and 2M respectively. Both are combined in such a way that their similar poles are same side. The time period in this case is ‘T1’ .If polarity of one of the magnets is reversed its period becomes ‘T2’ then find out ratio of their time periods T1/T2.
- a)√3
- b)1/√3
- c)1
- d)1/3
Correct answer is option 'B'. Can you explain this answer?
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Magnetic moments of two identical magnets are M and 2M respectively. B...
Case 1:
Msystem = M + 2M = 3M
Isystem = I + I = 2I
Case 2:
Msystem = 2M – M = M
Isystem = 2I
Msystem = M + 2M = 3M
Isystem = I + I = 2I
Case 2:
Msystem = 2M – M = M
Isystem = 2I
Most Upvoted Answer
Magnetic moments of two identical magnets are M and 2M respectively. B...
To find the time period of the combined magnets, we need to consider the torque acting on them.
When two magnets are combined such that their similar poles are on the same side, they experience a torque that tries to align them in the same direction. This torque can be calculated using the formula:
τ = μ × B
Where:
τ is the torque
μ is the magnetic moment
B is the magnetic field
Since the magnets are identical, they have the same magnetic field B acting on them. Let's assume this magnetic field is B.
For the magnet with magnetic moment M, the torque is τ1 = M × B
For the magnet with magnetic moment 2M, the torque is τ2 = 2M × B
The net torque acting on the combined system is the sum of the individual torques, so:
τ_net = τ1 + τ2 = (M × B) + (2M × B) = 3M × B
The time period T is related to the torque by the equation:
T = 2π/ω
Where ω is the angular acceleration. The angular acceleration can be calculated using the torque:
ω = τ_net / I
Where I is the moment of inertia of the combined system.
Since the magnets are identical, their moment of inertia can be considered as the sum of their individual moments of inertia:
I = I1 + I2 = 2I1
The moment of inertia of a magnet is given by:
I1 = 1/2 × (m × r^2)
Where m is the mass of the magnet and r is the distance from the axis of rotation.
Since the magnets are identical, they have the same mass m and the same distance r from the axis of rotation. Let's assume these values are m and r respectively.
I1 = 1/2 × (m × r^2)
I = 2I1 = 2 × (1/2 × m × r^2) = m × r^2
Now we can calculate the angular acceleration:
ω = τ_net / I = (3M × B) / (m × r^2)
Finally, we can substitute this angular acceleration into the equation for the time period:
T = 2π / ω = 2π / ((3M × B) / (m × r^2))
Simplifying this equation, we get:
T = (2π × m × r^2) / (3M × B)
Therefore, the time period of the combined magnets is (2π × m × r^2) / (3M × B).
When two magnets are combined such that their similar poles are on the same side, they experience a torque that tries to align them in the same direction. This torque can be calculated using the formula:
τ = μ × B
Where:
τ is the torque
μ is the magnetic moment
B is the magnetic field
Since the magnets are identical, they have the same magnetic field B acting on them. Let's assume this magnetic field is B.
For the magnet with magnetic moment M, the torque is τ1 = M × B
For the magnet with magnetic moment 2M, the torque is τ2 = 2M × B
The net torque acting on the combined system is the sum of the individual torques, so:
τ_net = τ1 + τ2 = (M × B) + (2M × B) = 3M × B
The time period T is related to the torque by the equation:
T = 2π/ω
Where ω is the angular acceleration. The angular acceleration can be calculated using the torque:
ω = τ_net / I
Where I is the moment of inertia of the combined system.
Since the magnets are identical, their moment of inertia can be considered as the sum of their individual moments of inertia:
I = I1 + I2 = 2I1
The moment of inertia of a magnet is given by:
I1 = 1/2 × (m × r^2)
Where m is the mass of the magnet and r is the distance from the axis of rotation.
Since the magnets are identical, they have the same mass m and the same distance r from the axis of rotation. Let's assume these values are m and r respectively.
I1 = 1/2 × (m × r^2)
I = 2I1 = 2 × (1/2 × m × r^2) = m × r^2
Now we can calculate the angular acceleration:
ω = τ_net / I = (3M × B) / (m × r^2)
Finally, we can substitute this angular acceleration into the equation for the time period:
T = 2π / ω = 2π / ((3M × B) / (m × r^2))
Simplifying this equation, we get:
T = (2π × m × r^2) / (3M × B)
Therefore, the time period of the combined magnets is (2π × m × r^2) / (3M × B).
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Magnetic moments of two identical magnets are M and 2M respectively. Both are combined in such a way that their similar poles are same side. The time period in this case is ‘T1’ .If polarity of one of the magnets is reversed its period becomes ‘T2’ then find out ratio of their time periods T1/T2.a)√3b)1/√3c)1d)1/3Correct answer is option 'B'. Can you explain this answer?
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Magnetic moments of two identical magnets are M and 2M respectively. Both are combined in such a way that their similar poles are same side. The time period in this case is ‘T1’ .If polarity of one of the magnets is reversed its period becomes ‘T2’ then find out ratio of their time periods T1/T2.a)√3b)1/√3c)1d)1/3Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Magnetic moments of two identical magnets are M and 2M respectively. Both are combined in such a way that their similar poles are same side. The time period in this case is ‘T1’ .If polarity of one of the magnets is reversed its period becomes ‘T2’ then find out ratio of their time periods T1/T2.a)√3b)1/√3c)1d)1/3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Magnetic moments of two identical magnets are M and 2M respectively. Both are combined in such a way that their similar poles are same side. The time period in this case is ‘T1’ .If polarity of one of the magnets is reversed its period becomes ‘T2’ then find out ratio of their time periods T1/T2.a)√3b)1/√3c)1d)1/3Correct answer is option 'B'. Can you explain this answer?.
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