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If the velocity of light (c) gravitational constant( g) and planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system?
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Dimensions of Mass in New System
Given Fundamental Units:
- Velocity of light (c)
- Gravitational constant (g)
- Planck's constant (h)
Step 1: Determining Dimensions of Fundamental Units
- Velocity of light (c): [L][T]^-1
- Gravitational constant (g): [L]^3 [M]^-1 [T]^-2
- Planck's constant (h): [L]^2 [M] [T]^-1
Step 2: Forming Dimensional Equations for Mass
- Mass (M) can be represented as a combination of fundamental units:
M = [c]^a [g]^b [h]^c
- Equating dimensions on both sides:
[M] = [L]^a [T]^-a [L]^(3b) [M]^(-b) [T]^(-2b) [L]^(2c) [M]^c [T]^(-c)
Step 3: Solving for Dimensions of Mass
- Equating exponents of similar dimensions:
a + b + 2c = 0 (for [L])
-b + c = 0 (for [M])
-a - 2b - c = 0 (for [T])
Step 4: Solving the System of Equations
- Solving the above system of equations, we get:
a = -1, b = -1, c = -1
Step 5: Final Dimensional Equation for Mass
- Substituting the values of a, b, and c in the dimensional equation for mass:
[M] = [T]^-1
Therefore, in the new system with velocity of light, gravitational constant, and Planck's constant as fundamental units, the dimension of mass is [T]^-1.
Given Fundamental Units:
- Velocity of light (c)
- Gravitational constant (g)
- Planck's constant (h)
Step 1: Determining Dimensions of Fundamental Units
- Velocity of light (c): [L][T]^-1
- Gravitational constant (g): [L]^3 [M]^-1 [T]^-2
- Planck's constant (h): [L]^2 [M] [T]^-1
Step 2: Forming Dimensional Equations for Mass
- Mass (M) can be represented as a combination of fundamental units:
M = [c]^a [g]^b [h]^c
- Equating dimensions on both sides:
[M] = [L]^a [T]^-a [L]^(3b) [M]^(-b) [T]^(-2b) [L]^(2c) [M]^c [T]^(-c)
Step 3: Solving for Dimensions of Mass
- Equating exponents of similar dimensions:
a + b + 2c = 0 (for [L])
-b + c = 0 (for [M])
-a - 2b - c = 0 (for [T])
Step 4: Solving the System of Equations
- Solving the above system of equations, we get:
a = -1, b = -1, c = -1
Step 5: Final Dimensional Equation for Mass
- Substituting the values of a, b, and c in the dimensional equation for mass:
[M] = [T]^-1
Therefore, in the new system with velocity of light, gravitational constant, and Planck's constant as fundamental units, the dimension of mass is [T]^-1.
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If the velocity of light (c) gravitational constant( g) and planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system? for NEET 2025 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 planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity of light (c) gravitational constant( g) and planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system?.
If the velocity of light (c) gravitational constant( g) and planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system? for NEET 2025 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 planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity of light (c) gravitational constant( g) and planks constant (h) are chosen as fundamental units then find the dimensions of mass in new system?.
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