Question

Gravitational potential is defined as:

• A. work done by the gravitational force per unit area
• B. work done by the gravitational force per unit volume
• C. work done by the gravitational force per unit mass
• D. work done by the gravitational force per unit time

Hint:

Gravitational potential = work per unit mass to bring object from infinity.

Answer 1

The Correct Option is C

To understand the correct definition of gravitational potential, let's analyze the concept step by step:

1. Understanding Gravitational Potential:
Gravitational potential at a point in a gravitational field represents the work done against the gravitational force to bring a unit mass from infinity to that point.

2. Key Features:

• It's a scalar quantity (has magnitude but no direction)
• Measured in joules per kilogram (J/kg)
• Describes the potential energy per unit mass

3. Mathematical Definition:
The gravitational potential V at a point is given by: 

V = W/m 

Where:

• W = work done against gravity
• m = mass of the object

4. Why "Per Unit Mass" is Correct:
Gravitational potential is fundamentally:

• Not related to area (eliminates Option A)
• Not a volumetric measure (eliminates Option B)
• Independent of time (eliminates Option D)
• Always defined per unit mass (makes Option C correct)

5. Physical Significance:
This definition allows us to:

• Compare potential at different points in a field
• Calculate potential energy for any mass (PE = mV)
• Determine gravitational field strength (g = -dV/dr)

Final Answer:
Gravitational potential is defined as work done by the gravitational force per unit mass.