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If G is the gravitational constant and g is the acceleration due to gravity, the unit of G/g is
- a)kg m-1
- b)kg m-2
- c)kg m
- d)kg-1 m2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If G is the gravitational constant and g is the acceleration due to gr...
The correct answer is option 4) i.e. kg-1 m2
Concept:
- Gravitational constant, G: G is a physical constant and therefore is universal in nature and has a constant value everywhere.
- The value of G does not change with respect to time or place and is equivalent to 6.674 × 10-11 N m2 kg-2
- The SI unit of G is N m2 kg-2
- Acceleration due to gravity, g: It isthe acceleration of a body due to the force exerted from the earth's gravity.
- It has a constant value of 9.8 m/s2 within the surface of Earth.
- The SI unit of g is m s-2
Explanation:
The unit of G = N m2 kg-2 = (mass × acceleration)m2 kg-2 = (kg × m/s2)m2 kg-2 (∵ N is the SI unit of force)
The unit of G = N m2 kg-2 = (mass × acceleration)m2 kg-2 = (kg × m/s2)m2 kg-2 (∵ N is the SI unit of force)
The unit of g = ms-2
Ratio, 
kg-1 m2
kg-1 m2Most Upvoted Answer
If G is the gravitational constant and g is the acceleration due to gr...
Understanding G and g
The gravitational constant (G) and the acceleration due to gravity (g) are fundamental constants in physics.
Definitions:
- G (Gravitational Constant): A proportionality constant used in the equation of gravitation, with a value of approximately 6.674 × 10^-11 N m²/kg².
- g (Acceleration due to Gravity): Represents the acceleration experienced by an object due to the gravitational force near the Earth's surface, approximately 9.81 m/s².
Units of G and g
- Unit of G: The unit of G is N m²/kg². In terms of base units, this is expressed as:
- N (Newton) = kg m/s²
- Therefore, G = (kg m/s²) m²/(kg²) = kg m²/(kg² s²) = m³/(kg s²).
- Unit of g: The unit of g is simply m/s².
Calculating G/g
To find the unit of G/g, we perform the following calculation:
- G/g = (m³/(kg s²)) / (m/s²)
This can be simplified as follows:
- G/g = (m³/(kg s²)) * (s²/m) = m²/kg.
This leads us to:
- G/g = kg⁻¹ m².
Conclusion
Thus, the unit of G/g is indeed kg⁻¹ m², confirming that the correct answer is option 'D'.
The gravitational constant (G) and the acceleration due to gravity (g) are fundamental constants in physics.
Definitions:
- G (Gravitational Constant): A proportionality constant used in the equation of gravitation, with a value of approximately 6.674 × 10^-11 N m²/kg².
- g (Acceleration due to Gravity): Represents the acceleration experienced by an object due to the gravitational force near the Earth's surface, approximately 9.81 m/s².
Units of G and g
- Unit of G: The unit of G is N m²/kg². In terms of base units, this is expressed as:
- N (Newton) = kg m/s²
- Therefore, G = (kg m/s²) m²/(kg²) = kg m²/(kg² s²) = m³/(kg s²).
- Unit of g: The unit of g is simply m/s².
Calculating G/g
To find the unit of G/g, we perform the following calculation:
- G/g = (m³/(kg s²)) / (m/s²)
This can be simplified as follows:
- G/g = (m³/(kg s²)) * (s²/m) = m²/kg.
This leads us to:
- G/g = kg⁻¹ m².
Conclusion
Thus, the unit of G/g is indeed kg⁻¹ m², confirming that the correct answer is option 'D'.
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If G is the gravitational constant and g is the acceleration due to gravity, the unit of G/g isa)kg m-1b)kg m-2c)kg md)kg-1m2Correct answer is option 'D'. Can you explain this answer?
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