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A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration is
- a)t/2
- b)t
- c)2t
- d)4t
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A particle is at a distance r from the axis of rotation. A given torqu...
We know that from some torque t, angular acceleration a produced can be find by,
t = I a, where I is moment of inertia = mr2
Thus we get a = t / mr2
Now we have 2m and r/2
Thus a = t / mr2 = T / 2m(r/2)2
Thus we get T = t/2
t = I a, where I is moment of inertia = mr2
Thus we get a = t / mr2
Now we have 2m and r/2
Thus a = t / mr2 = T / 2m(r/2)2
Thus we get T = t/2
Most Upvoted Answer
A particle is at a distance r from the axis of rotation. A given torqu...
Torque and Angular Acceleration
Torque, denoted by 'τ', is the measure of the force that can cause an object to rotate about an axis. It is given by the product of the force applied and the perpendicular distance from the axis of rotation. Mathematically, torque is represented as τ = r × F, where 'r' is the distance from the axis of rotation and 'F' is the force applied.
Angular acceleration, denoted by 'α', represents the rate of change of angular velocity. It is related to torque and the moment of inertia of the object. Mathematically, angular acceleration is given by α = τ / I, where 'I' is the moment of inertia of the object.
Effect of Changing Mass and Distance
When the mass of the particle is doubled and its distance from the axis is halved, we need to determine the effect on the torque required to produce the same angular acceleration.
Let's assume the original mass of the particle is 'm' and the original distance from the axis is 'r'. The original torque required to produce the given angular acceleration is 't'.
When the mass is doubled, the new mass becomes '2m'. When the distance is halved, the new distance becomes 'r/2'.
Calculating the New Torque
To find the new torque required, we can use the formula τ = r × F. Since the force remains the same, we can compare the torques using the distances.
Original torque, t = r × F
New torque, t' = (r/2) × F
Comparing the original and new torques:
t' = (r/2) × F = (1/2) × (r × F) = (1/2) × t
Hence, the new torque required to produce the same angular acceleration is half of the original torque.
Conclusion
The correct answer is option 'A', t/2. When the mass of the particle is doubled and its distance from the axis is halved, the torque required to produce the same angular acceleration is reduced by half.
Torque, denoted by 'τ', is the measure of the force that can cause an object to rotate about an axis. It is given by the product of the force applied and the perpendicular distance from the axis of rotation. Mathematically, torque is represented as τ = r × F, where 'r' is the distance from the axis of rotation and 'F' is the force applied.
Angular acceleration, denoted by 'α', represents the rate of change of angular velocity. It is related to torque and the moment of inertia of the object. Mathematically, angular acceleration is given by α = τ / I, where 'I' is the moment of inertia of the object.
Effect of Changing Mass and Distance
When the mass of the particle is doubled and its distance from the axis is halved, we need to determine the effect on the torque required to produce the same angular acceleration.
Let's assume the original mass of the particle is 'm' and the original distance from the axis is 'r'. The original torque required to produce the given angular acceleration is 't'.
When the mass is doubled, the new mass becomes '2m'. When the distance is halved, the new distance becomes 'r/2'.
Calculating the New Torque
To find the new torque required, we can use the formula τ = r × F. Since the force remains the same, we can compare the torques using the distances.
Original torque, t = r × F
New torque, t' = (r/2) × F
Comparing the original and new torques:
t' = (r/2) × F = (1/2) × (r × F) = (1/2) × t
Hence, the new torque required to produce the same angular acceleration is half of the original torque.
Conclusion
The correct answer is option 'A', t/2. When the mass of the particle is doubled and its distance from the axis is halved, the torque required to produce the same angular acceleration is reduced by half.
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A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer?.
A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer?.
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A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A particle is at a distance r from the axis of rotation. A given torque t produces some angular acceleration in it. If the mass of the particle is doubled and its distance from the axis is halved, the value of torque to produce the same angular acceleration isa)t/2b)tc)2td)4tCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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