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The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is?
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The potential energy of a particle Varies with distance x from a fixed...
Understanding the Problem:
We are given the potential energy of a particle, which varies with distance x from a fixed point. The equation for the potential energy is given as u = A√x by x², where A and B are constants.
Breaking Down the Equation:
Let's break down the equation to understand it better:
u = A√x by x²
Here, A is a constant and represents the amplitude of the potential energy.
√x represents the square root of x, which means the potential energy is proportional to the square root of x.
x² represents the square of x, which means the potential energy is inversely proportional to the square of x.
Finding the Dimension of AB²:
To find the dimensions of AB², we need to analyze the dimensions of each term in the equation.
Dimension of u:
The dimension of potential energy, u, is given by [M L² T⁻²], where M represents mass, L represents length, and T represents time.
Dimension of √x:
The dimension of √x is given by [L^(1/2)], as it is the square root of length.
Dimension of x²:
The dimension of x² is given by [L²], as it is the square of length.
Combining the Dimensions:
Now, let's combine the dimensions of each term in the equation to find the dimension of AB².
The dimension of u is [M L² T⁻²].
The dimension of √x is [L^(1/2)].
The dimension of x² is [L²].
Since u = A√x by x², the dimensions on both sides of the equation should be equal.
Equating the Dimensions:
Equating the dimensions, we have:
[M L² T⁻²] = A[L^(1/2)]/[L²]
Simplifying the equation, we get:
[M L² T⁻²] = A[L^(-3/2)]
Now, to balance the dimensions on both sides of the equation, we equate the exponents of each dimension:
1. Equating the dimensions of mass:
1 = 0
This implies that the dimensions of mass are balanced.
2. Equating the dimensions of length:
2 = -3/2
This implies that the dimensions of length are not balanced.
3. Equating the dimensions of time:
T⁻² = 0
This implies that the dimensions of time are balanced.
Conclusion:
From the analysis above, we can conclude that the dimensions of AB² cannot be determined, as the dimensions of length are not balanced in the given equation.
We are given the potential energy of a particle, which varies with distance x from a fixed point. The equation for the potential energy is given as u = A√x by x², where A and B are constants.
Breaking Down the Equation:
Let's break down the equation to understand it better:
u = A√x by x²
Here, A is a constant and represents the amplitude of the potential energy.
√x represents the square root of x, which means the potential energy is proportional to the square root of x.
x² represents the square of x, which means the potential energy is inversely proportional to the square of x.
Finding the Dimension of AB²:
To find the dimensions of AB², we need to analyze the dimensions of each term in the equation.
Dimension of u:
The dimension of potential energy, u, is given by [M L² T⁻²], where M represents mass, L represents length, and T represents time.
Dimension of √x:
The dimension of √x is given by [L^(1/2)], as it is the square root of length.
Dimension of x²:
The dimension of x² is given by [L²], as it is the square of length.
Combining the Dimensions:
Now, let's combine the dimensions of each term in the equation to find the dimension of AB².
The dimension of u is [M L² T⁻²].
The dimension of √x is [L^(1/2)].
The dimension of x² is [L²].
Since u = A√x by x², the dimensions on both sides of the equation should be equal.
Equating the Dimensions:
Equating the dimensions, we have:
[M L² T⁻²] = A[L^(1/2)]/[L²]
Simplifying the equation, we get:
[M L² T⁻²] = A[L^(-3/2)]
Now, to balance the dimensions on both sides of the equation, we equate the exponents of each dimension:
1. Equating the dimensions of mass:
1 = 0
This implies that the dimensions of mass are balanced.
2. Equating the dimensions of length:
2 = -3/2
This implies that the dimensions of length are not balanced.
3. Equating the dimensions of time:
T⁻² = 0
This implies that the dimensions of time are balanced.
Conclusion:
From the analysis above, we can conclude that the dimensions of AB² cannot be determined, as the dimensions of length are not balanced in the given equation.
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The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is?
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The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is?.
The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The potential energy of a particle Varies with distance x from a fixed point as u = A√x by x bsq where A and B are constants.the dimension of ABsq is?.
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