Gravitational potential and gravitational potential energy are fundamental concepts in physics, particularly in the study of gravitation and celestial mechanics. While they are closely related, they have distinct meanings and applications. Below is a detailed comparison in question-answer format, along with multiple-choice questions (MCQs) and explanations.
🔹 What is Gravitational Potential?
Gravitational potential at a point in a gravitational field is the gravitational potential energy per unit mass at that point.
Formula:
V = −GM/r
- V = Gravitational potential
- G = Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
- M = Mass of the body creating the gravitational field
- r = Distance from the center of the mass
Key Characteristics:
- It is a scalar quantity.
- It represents work done to bring a unit mass from infinity to a point in the field.
- It is always negative because gravitational force is attractive.
- It depends on the mass of the attracting body and the distance from it.
🔹 What is Gravitational Potential Energy?
Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field.
Formula:
U = −GMm/r
- U = Gravitational potential energy
- m = Mass of the object
- G = Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²)
- M = Mass of the body creating the gravitational field
- r = Distance from the center of the mass
Key Characteristics:
- It is a scalar quantity.
- It depends on both the mass of the object and the attracting mass.
- It is also negative because work is required to separate two masses.
- It varies with the distance between the two masses.
Difference Between Gravitational Potential and Gravitational Potential Energy
| Gravitational Potential | Gravitational Potential Energy |
| Gravitational potential at any point is defined as the work done in moving a unit mass from infinity to that point against the gravitational field. It determines the direction of motion of a body in the gravitational field of another body. Gravitational Potential is equal to the potential energy of the unit mass kept at that point. | Gravitational Potential Energy is defined as the energy stored in an object that is held in a vertical position due to the force of gravity working on it to pull it down. The amount of gravitational potential energy depends on the mass and height of an object. |
| The Formula for gravitational potential is, V = -GM/r. | The Formula for gravitational potential energy is, U = mgh. |
| The unit of gravitational potential is Joules/kg. | The unit of gravitational potential energy is Joules. |
| It is represented by V. | It is represented by U. |
| It is always negative. | It is always positive. |
| It is maximum at infinity. | It is zero at infinity. |
| It is minimum at the center of the earth. | It is minimum at the surface of the object. |
| The dimensional formula of gravitational potential is, [M0L2T-2]. | The dimensional formula of gravitational potential energy is, [M1L2T-2] |
🔹 FAQs (Frequently Asked Questions)
Q1: Why is gravitational potential energy always negative?
A: Since work is required to move an object against gravity (away from the source), energy is defined relative to infinity, making it negative in bound systems.
Q2: Can gravitational potential be positive?
A: No, because gravity is always attractive, and potential energy decreases as mass moves closer.
Q3: What is the difference between gravitational potential and gravitational field strength?
A: Gravitational potential refers to the work done per unit mass, while gravitational field strength is the force per unit mass.
Q4: How does gravitational potential energy change with height?
A: It increases as the object moves further from the gravitational source.
🔹 Multiple Choice Questions (MCQs)
Q1: What is the unit of gravitational potential?
A) Newton (N)
B) Joule (J)
C) Joule per kilogram (J/kg)
D) Newton per kilogram (N/kg)
Answer: C) Joule per kilogram (J/kg)
Explanation: Gravitational potential is energy per unit mass, hence J/kg.
Q2: Which of the following affects gravitational potential energy the most?
A) Shape of the object
B) Mass of the object
C) Distance from the source
D) Both B and C
Answer: D) Both B and C
Explanation: Gravitational potential energy depends on both the mass of the object and its distance from the gravitational source.
Q3: What happens to the gravitational potential as we go deeper into the Earth?
A) Increases
B) Decreases
C) Remains constant
D) First increases, then decreases
Answer: B) Decreases
Explanation: The gravitational potential decreases as we move closer to the center of the Earth.
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