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The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] is
- a)LT–1
- b)LT–2
- c)LT–3
- d)LT–4
Correct answer is option 'D'. Can you explain this answer?
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The position of a particle along the y- axis is y = Pt4 + Q. For the e...
Dimensional Consistency of an Equation:
The dimensional consistency of an equation means that all the terms in the equation have the same dimensions on both sides. In other words, the dimensions of the variables on both sides of the equation should be the same. If the dimensions are not the same, then the equation is not dimensionally consistent, and it may not make any physical sense.
Given Equation:
y = Pt^4
In this equation, y represents the position of a particle along the y-axis, t represents time, and P is a constant.
Dimensional Analysis:
In the SI system of units, the dimension of length is represented by [L], and the dimension of time is represented by [T]. Let's determine the dimensions of each term in the equation.
- The dimension of y is [L].
- The dimension of t^4 is [T]^4.
- The dimension of P is unknown, so let's represent it by [M]^a[L]^b[T]^c, where a, b, and c are unknown exponents.
Now, we can rewrite the given equation in terms of dimensions as follows:
[L] = [M]^a[L]^b[T]^c [T]^4
Equating the dimensions of both sides of the equation, we get:
[L] = [M]^a[L]^(b+c) [T]^4
Now, equating the dimensions of length on both sides, we get:
1 = [M]^a [T]^(4c)
Equating the dimensions of time on both sides, we get:
0 = b + c
Solving the above two equations, we get:
a = 1, b = 0, and c = 0
Therefore, the dimension of P is [M]^1[L]^0[T]^0, which simplifies to [M][T]^0[L]^0. As [T]^0 and [L]^0 both equal to 1, the dimension of P is simply [M], which represents mass.
Answer:
Therefore, the dimension of P in terms of length [L] and time [T] is LT⁴. The correct option is D.
The dimensional consistency of an equation means that all the terms in the equation have the same dimensions on both sides. In other words, the dimensions of the variables on both sides of the equation should be the same. If the dimensions are not the same, then the equation is not dimensionally consistent, and it may not make any physical sense.
Given Equation:
y = Pt^4
In this equation, y represents the position of a particle along the y-axis, t represents time, and P is a constant.
Dimensional Analysis:
In the SI system of units, the dimension of length is represented by [L], and the dimension of time is represented by [T]. Let's determine the dimensions of each term in the equation.
- The dimension of y is [L].
- The dimension of t^4 is [T]^4.
- The dimension of P is unknown, so let's represent it by [M]^a[L]^b[T]^c, where a, b, and c are unknown exponents.
Now, we can rewrite the given equation in terms of dimensions as follows:
[L] = [M]^a[L]^b[T]^c [T]^4
Equating the dimensions of both sides of the equation, we get:
[L] = [M]^a[L]^(b+c) [T]^4
Now, equating the dimensions of length on both sides, we get:
1 = [M]^a [T]^(4c)
Equating the dimensions of time on both sides, we get:
0 = b + c
Solving the above two equations, we get:
a = 1, b = 0, and c = 0
Therefore, the dimension of P is [M]^1[L]^0[T]^0, which simplifies to [M][T]^0[L]^0. As [T]^0 and [L]^0 both equal to 1, the dimension of P is simply [M], which represents mass.
Answer:
Therefore, the dimension of P in terms of length [L] and time [T] is LT⁴. The correct option is D.
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The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer?
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The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer?.
The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position of a particle along the y- axis is y = Pt4 + Q. For the equation to be dimensionally consistent, the dimension of P in terms of length [L] and time [T] isa)LT–1b)LT–2c)LT–3d)LT–4Correct answer is option 'D'. Can you explain this answer?.
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