The value of acceleration due to gravity on the surface of earth is x. At alttitude of ‘h’ from the surface of earth, its value is y. If ‘R’ is the radius of earth, then the value of h is

To solve the question, we need to determine the height h where the value of acceleration due to gravity changes from x (on the Earth's surface) to y (at an altitude h above the surface).

Formula for Acceleration Due to Gravity

The value of acceleration due to gravity is calculated using the formula:

g = (GM) / r²

• G: Universal gravitational constant
• M: Mass of the Earth
• r: Distance from the center of the Earth

Steps to Calculate the Height

1. Gravitational acceleration on the Earth's surface:

The value of acceleration due to gravity is given as:

x = (GM) / R² (where R is the Earth's radius).

1. Gravitational acceleration at height h:

The value of acceleration due to gravity is expressed as:

y = (GM) / (R + h)²

1. Relating the two values:

From the two expressions above:

x / y = (R + h)² / R²

1. Cross-multiplying:

x × R² = y × (R + h)²

1. Solving for h:

Taking the square root of both sides:

√(x / y) = (R + h) / R

Rearranging to isolate h:

R + h = R × √(x / y)

h = R × (√(x / y) - 1)

Final Expression

Thus, the height h at which the value of acceleration due to gravity is reduced from x to y is given by:

h = R × (√(x / y) - 1)