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Choose the correct statements for the case of a one dimensional simple harmonic motion.
- a)The points at which the gradient of potential are the points of stable equilibrium
- b)Force is a negative gradient of the potential
- c)The points with a negative gradient of the potential are the points of unstable equilibrium
- d)Force is a negative gradient of velocity
Correct answer is option 'A,B,C'. Can you explain this answer?
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Choose the correct statements for the case of a one dimensional simple...
The correct answers are: Force is a negative gradient of the potential, The points at which the gradient of potential are the points of stable equilibrium, The points with a negative gradient of the potential are the points of unstable equilibrium
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Choose the correct statements for the case of a one dimensional simple...
One Dimensional Simple Harmonic Motion
Simple harmonic motion (SHM) refers to the repetitive back-and-forth motion of an object about a central position, where the restoring force is directly proportional to the displacement from the equilibrium position. In the case of one-dimensional SHM, the motion occurs along a straight line.
The Gradient of Potential in Simple Harmonic Motion
The potential energy function in SHM is given by U(x) = (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position. The gradient of the potential, ∇U(x), represents the rate of change of potential energy with respect to displacement.
Points of Stable Equilibrium
Stable equilibrium refers to a situation where an object, when displaced slightly from its equilibrium position, experiences a restoring force that brings it back towards the equilibrium position. Mathematically, stable equilibrium corresponds to points where the potential energy is at a minimum.
Points of Unstable Equilibrium
Unstable equilibrium refers to a situation where an object, when displaced slightly from its equilibrium position, experiences a restoring force that pushes it further away from the equilibrium position. Mathematically, unstable equilibrium corresponds to points where the potential energy is at a maximum.
Relationship between Force and Potential
The force acting on an object in SHM is given by F(x) = -dU(x)/dx, where dU(x)/dx represents the derivative of the potential energy function with respect to displacement. This relationship implies that the force is the negative gradient of the potential.
Correct Statements
Based on the above explanations, the correct statements for the case of one-dimensional SHM are:
a) The points at which the gradient of potential are the points of stable equilibrium. This is true because the gradient of potential represents the rate of change of potential energy, and points of stable equilibrium correspond to potential energy minima.
b) Force is a negative gradient of the potential. This is true because the force acting on an object is given by the negative derivative of the potential energy with respect to displacement.
c) The points with a negative gradient of the potential are the points of unstable equilibrium. This is true because points of unstable equilibrium correspond to potential energy maxima, and the negative gradient of the potential indicates a force that pushes the object away from the equilibrium position.
Therefore, the correct answer is option 'A, B, C'.
Simple harmonic motion (SHM) refers to the repetitive back-and-forth motion of an object about a central position, where the restoring force is directly proportional to the displacement from the equilibrium position. In the case of one-dimensional SHM, the motion occurs along a straight line.
The Gradient of Potential in Simple Harmonic Motion
The potential energy function in SHM is given by U(x) = (1/2)kx², where k is the spring constant and x is the displacement from the equilibrium position. The gradient of the potential, ∇U(x), represents the rate of change of potential energy with respect to displacement.
Points of Stable Equilibrium
Stable equilibrium refers to a situation where an object, when displaced slightly from its equilibrium position, experiences a restoring force that brings it back towards the equilibrium position. Mathematically, stable equilibrium corresponds to points where the potential energy is at a minimum.
Points of Unstable Equilibrium
Unstable equilibrium refers to a situation where an object, when displaced slightly from its equilibrium position, experiences a restoring force that pushes it further away from the equilibrium position. Mathematically, unstable equilibrium corresponds to points where the potential energy is at a maximum.
Relationship between Force and Potential
The force acting on an object in SHM is given by F(x) = -dU(x)/dx, where dU(x)/dx represents the derivative of the potential energy function with respect to displacement. This relationship implies that the force is the negative gradient of the potential.
Correct Statements
Based on the above explanations, the correct statements for the case of one-dimensional SHM are:
a) The points at which the gradient of potential are the points of stable equilibrium. This is true because the gradient of potential represents the rate of change of potential energy, and points of stable equilibrium correspond to potential energy minima.
b) Force is a negative gradient of the potential. This is true because the force acting on an object is given by the negative derivative of the potential energy with respect to displacement.
c) The points with a negative gradient of the potential are the points of unstable equilibrium. This is true because points of unstable equilibrium correspond to potential energy maxima, and the negative gradient of the potential indicates a force that pushes the object away from the equilibrium position.
Therefore, the correct answer is option 'A, B, C'.
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Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer?
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Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer?.
Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer?.
Solutions for Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
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Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer?, a detailed solution for Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? has been provided alongside types of Choose the correct statements for the case of a one dimensional simple harmonic motion.a)The points at which the gradient of potential are the points of stable equilibriumb)Force is a negative gradient of the potentialc)The points with a negative gradient of the potential are the points of unstable equilibriumd)Force is a negative gradient of velocityCorrect answer is option 'A,B,C'. Can you explain this answer? theory, EduRev gives you an
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