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If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass is
- a)h−1/2G1/2C0
- b)h1/2C1/2G−1/2
- c)h−1/2C1/2G−1/2
- d)h−1/2C−1/2G−1/2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If C the velocity of light, h Planck's constant and G gravitational co...
Understanding the Problem
To derive the dimensional formula of mass using C (velocity of light), h (Planck's constant), and G (gravitational constant), we start with their respective dimensions:
- C (Velocity of Light): [C] = L^1 T^-1
- h (Planck's Constant): [h] = M^1 L^2 T^-1
- G (Gravitational Constant): [G] = M^-1 L^3 T^-2
Dimensional Analysis
We want to express mass (M) in terms of C, h, and G. Let's assume the dimensional formula of mass is given by:
M = h^a C^b G^c
This translates to:
M^1 = (M^1 L^2 T^-1)^a (L^1 T^-1)^b (M^-1 L^3 T^-2)^c
Equating Dimensions
Now, we can equate the dimensions of mass, length, and time on both sides:
1. For Mass (M): 1 = a - c
2. For Length (L): 0 = 2a + b + 3c
3. For Time (T): 0 = -a - b - 2c
Solving the Equations
From the first equation, we have:
c = a - 1
Substituting c in the second and third equations gives us a system of equations. After solving these equations, we find:
- a = 1/2
- b = 1/2
- c = -1/2
Final Result
Substituting back into our assumed formula gives us:
M = h^(1/2) C^(1/2) G^(-1/2)
Thus, the correct answer is option 'b':
Answer: h^(1/2) C^(1/2) G^(-1/2)
To derive the dimensional formula of mass using C (velocity of light), h (Planck's constant), and G (gravitational constant), we start with their respective dimensions:
- C (Velocity of Light): [C] = L^1 T^-1
- h (Planck's Constant): [h] = M^1 L^2 T^-1
- G (Gravitational Constant): [G] = M^-1 L^3 T^-2
Dimensional Analysis
We want to express mass (M) in terms of C, h, and G. Let's assume the dimensional formula of mass is given by:
M = h^a C^b G^c
This translates to:
M^1 = (M^1 L^2 T^-1)^a (L^1 T^-1)^b (M^-1 L^3 T^-2)^c
Equating Dimensions
Now, we can equate the dimensions of mass, length, and time on both sides:
1. For Mass (M): 1 = a - c
2. For Length (L): 0 = 2a + b + 3c
3. For Time (T): 0 = -a - b - 2c
Solving the Equations
From the first equation, we have:
c = a - 1
Substituting c in the second and third equations gives us a system of equations. After solving these equations, we find:
- a = 1/2
- b = 1/2
- c = -1/2
Final Result
Substituting back into our assumed formula gives us:
M = h^(1/2) C^(1/2) G^(-1/2)
Thus, the correct answer is option 'b':
Answer: h^(1/2) C^(1/2) G^(-1/2)
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Community Answer
If C the velocity of light, h Planck's constant and G gravitational co...
Let,
Comparing the coefficients M,L,T, of both sides we get
Comparing the coefficients M,L,T, of both sides we get
b−c=1
a + 2b + 3c = 0
−(a + b + 2c) = 0
Solve the Eqs. (ii), (iii) and (iv), we get
So,
M=h1/2C1/2G−1/2
a + 2b + 3c = 0
−(a + b + 2c) = 0
Solve the Eqs. (ii), (iii) and (iv), we get
So,
M=h1/2C1/2G−1/2
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Question Description
If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isa)h−1/2G1/2C0b)h1/2C1/2G−1/2c)h−1/2C1/2G−1/2d)h−1/2C−1/2G−1/2Correct answer is option 'B'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isa)h−1/2G1/2C0b)h1/2C1/2G−1/2c)h−1/2C1/2G−1/2d)h−1/2C−1/2G−1/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isa)h−1/2G1/2C0b)h1/2C1/2G−1/2c)h−1/2C1/2G−1/2d)h−1/2C−1/2G−1/2Correct answer is option 'B'. Can you explain this answer?.
If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isa)h−1/2G1/2C0b)h1/2C1/2G−1/2c)h−1/2C1/2G−1/2d)h−1/2C−1/2G−1/2Correct answer is option 'B'. Can you explain this answer? for NEET 2026 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isa)h−1/2G1/2C0b)h1/2C1/2G−1/2c)h−1/2C1/2G−1/2d)h−1/2C−1/2G−1/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If C the velocity of light, h Planck's constant and G gravitational constant are taken as fundamental quantities, then the dimensional formula of mass isa)h−1/2G1/2C0b)h1/2C1/2G−1/2c)h−1/2C1/2G−1/2d)h−1/2C−1/2G−1/2Correct answer is option 'B'. Can you explain this answer?.
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