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A particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6 , k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of η is _______.
Correct answer is '4'. Can you explain this answer?
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A particle of mass m moves wider the action of a central force whose p...
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A particle of mass m moves wider the action of a central force whose p...
The potential energy function provided is U(r) = kr^6, where k is a constant.
To determine the force experienced by the particle, we need to calculate the negative gradient of the potential energy function. The force is given by the equation F = -∇U, where ∇ represents the gradient operator.
Taking the derivative of U(r) with respect to r, we get:
dU/dr = 6kr^5
Now, we can calculate the force by taking the negative gradient:
F = -∇U = -dU/dr = -6kr^5
Therefore, the force experienced by the particle is F = -6kr^5.
To determine the force experienced by the particle, we need to calculate the negative gradient of the potential energy function. The force is given by the equation F = -∇U, where ∇ represents the gradient operator.
Taking the derivative of U(r) with respect to r, we get:
dU/dr = 6kr^5
Now, we can calculate the force by taking the negative gradient:
F = -∇U = -dU/dr = -6kr^5
Therefore, the force experienced by the particle is F = -6kr^5.
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A particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. Can you explain this answer?
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A particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. 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 particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. 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 particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. Can you explain this answer?.
A particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. 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 particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. 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 particle of mass m moves wider the action of a central force whose potential energy is U(r) = kr6, k > O. If the orbit be a circle of radius a about origin, then the total energy is ηka6. The value of ηis _______.Correct answer is '4'. Can you explain this answer?.
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