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If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.?
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If the velocity of light (c), gravitational constant (G) and Planck's ...
Introduction
When velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, the system is known as a natural system of units or Planck units.
Dimension of Mass in Planck units
In Planck units, the dimension of mass can be found by using dimensional analysis. The dimensional formula of mass is [M].
Formula for Planck units
The Planck units can be expressed as:
c = G = h = 1
Dimensional formula of velocity of light
The dimensional formula of velocity of light is [L][T]^-1.
Dimensional formula of gravitational constant
The dimensional formula of gravitational constant is [L]^3[M]^-1[T]^-2.
Dimensional formula of Planck's constant
The dimensional formula of Planck's constant is [L]^2[M][T]^-1.
Substituting the Planck units in the dimensional formula of gravitational constant
Substituting Planck's units in the dimensional formula of gravitational constant, we get:
1 = [L]^3[M]^-1[T]^-2
Simplifying the above equation,
[L] = [M]^[1/3][T]^[2/3]
Substituting the Planck units in the dimensional formula of Planck's constant
Substituting Planck's units in the dimensional formula of Planck's constant, we get:
1 = [L]^2[M][T]^-1
Simplifying the above equation,
[M] = [L]^-2[T]
Substituting the Planck units in the dimensional formula of velocity of light
Substituting Planck's units in the dimensional formula of velocity of light, we get:
1 = [L][T]^-1
Simplifying the above equation,
[L] = [T]
Dimension of mass in Planck units
Substituting the value of [L] in the dimensional formula of mass, we get:
[M] = [T]^-3/2
Therefore, the dimension of mass in the Planck units system is [T]^-3/2.
When velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, the system is known as a natural system of units or Planck units.
Dimension of Mass in Planck units
In Planck units, the dimension of mass can be found by using dimensional analysis. The dimensional formula of mass is [M].
Formula for Planck units
The Planck units can be expressed as:
c = G = h = 1
Dimensional formula of velocity of light
The dimensional formula of velocity of light is [L][T]^-1.
Dimensional formula of gravitational constant
The dimensional formula of gravitational constant is [L]^3[M]^-1[T]^-2.
Dimensional formula of Planck's constant
The dimensional formula of Planck's constant is [L]^2[M][T]^-1.
Substituting the Planck units in the dimensional formula of gravitational constant
Substituting Planck's units in the dimensional formula of gravitational constant, we get:
1 = [L]^3[M]^-1[T]^-2
Simplifying the above equation,
[L] = [M]^[1/3][T]^[2/3]
Substituting the Planck units in the dimensional formula of Planck's constant
Substituting Planck's units in the dimensional formula of Planck's constant, we get:
1 = [L]^2[M][T]^-1
Simplifying the above equation,
[M] = [L]^-2[T]
Substituting the Planck units in the dimensional formula of velocity of light
Substituting Planck's units in the dimensional formula of velocity of light, we get:
1 = [L][T]^-1
Simplifying the above equation,
[L] = [T]
Dimension of mass in Planck units
Substituting the value of [L] in the dimensional formula of mass, we get:
[M] = [T]^-3/2
Therefore, the dimension of mass in the Planck units system is [T]^-3/2.
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If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.?
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If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.?.
If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.?.
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