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If the velocity of light (c), gravitational constant (G), and Plank's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.?
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Dimension of Mass in the New System
The dimension of mass in the new system can be determined by expressing mass in terms of the chosen fundamental units - velocity of light (c), gravitational constant (G), and Planck's constant (h).
Step 1: Expressing Mass in Terms of Fundamental Units
- Mass (M) can be expressed as a combination of the fundamental units as:
M = (c^a) * (G^b) * (h^c)
where a, b, and c are the unknown exponents that need to be determined.
Step 2: Equating Dimensions
- The dimensions of mass, velocity, gravitational constant, and Planck's constant are as follows:
[M] = M^1
[c] = LT^-1
[G] = L^3 M^-1 T^-2
[h] = ML^2 T^-1
Step 3: Determining Exponents
- By equating dimensions, we get:
M^1 = (LT^-1)^a * (L^3 M^-1 T^-2)^b * (ML^2 T^-1)^c
Equating powers of M, L, and T, we get a = 0, b = 1/2, c = 1/2
Step 4: Final Expression for Mass
- Substituting the values of a, b, and c back into the expression for mass, we get:
M = sqrt(Gh/c)
Therefore, the dimension of mass in the new system, where the fundamental units are velocity of light, gravitational constant, and Planck's constant, is given by M = sqrt(Gh/c).
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If the velocity of light (c), gravitational constant (G), and Plank'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 Plank's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the velocity of light (c), gravitational constant (G), and Plank's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity of light (c), gravitational constant (G), and Plank'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 Plank's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the velocity of light (c), gravitational constant (G), and Plank's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the velocity of light (c), gravitational constant (G), and Plank's constant (h) are chosen as fundamental units, then find the dimension of mass in new system.?.
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