Gravitational Potential Energy

Step 1: The gravitational potential energy ( ) between two masses and separated by a distance is given by: Step 2: In this case, both masses are equal to , so the equation simplifies to: Step 3: Therefore, the correct answer is (B). \bigskip

The gravitational constant appears in Newton's law of gravitation: where: - is the force with dimensional formula
- and are masses with dimensional formula
- is the distance with dimensional formula
The dimensional formula of can be derived as follows: Substituting the dimensional formulas: Solving for : Thus, the dimensional formula of is: Therefore, comparing this with , we get: Thus, the correct values of , , and are .

The potential energy of an object of mass placed at a distance from the center of the Earth (i.e., on the surface of the Earth) is given by the gravitational potential energy formula: Where: - is the gravitational constant, - is the mass of the Earth, - is the mass of the object, - is the radius of the Earth. Thus, the correct answer is:

Step 1: Understanding the Concept:
Gravitational potential energy . For 1 kg mass, .

Step 2: Detailed Explanation:
and

Ratio =

Step 3: Final Answer:
The ratio is .

Concept:
• Total energy of satellite:

Step 1: Take magnitudes


Step 2: Ratio
Final Conclusion:
Option (B)

Step 1: Understanding the Concept:
Gravitational potential energy is the energy possessed by a mass due to its position in a gravitational field.
For a satellite orbiting the Earth, the potential energy is always negative, which indicates that it is a gravitationally bound system.
Step 2: Key Formula or Approach:
The formula for the gravitational potential energy of a satellite of mass orbiting a planet of mass at an orbital radius is given by:
Step 3: Detailed Explanation:
In this formula, the gravitational constant , the mass of the Earth , and the mass of the satellite are all positive constants.
When the orbital radius decreases, the denominator becomes smaller, which makes the magnitude of the fraction larger.
However, because of the negative sign in the formula, an increase in the magnitude means the actual value of the potential energy becomes more negative.
Becoming more negative corresponds to a mathematical decrease in the total value.
Step 4: Final Answer:
The gravitational potential energy decreases.