Question

The value of Acceleration due to Gravity at Height equal to half the radius of the earth is :

• A. 9/4g
• B. 4/9 g
• C. 2/3g
• D. 3/2g

Answer 1

Answer:

B. 4/9 g

• The acceleration due to gravity (g) on the Earth's surface is given by the formula g = GM/R², where G is the Universal Gravitational Constant, M is the mass of the Earth, and R is the radius of the Earth.

• When moving to a height h above the Earth's surface, the acceleration due to gravity (g') is calculated using the formula: g' = g * [R / (R + h)]².

• In this specific problem, the height h is given as half the radius of the Earth, so h = R/2.

• Substituting the value of h into the formula: g' = g * [R / (R + R/2)]².

• Simplifying the expression: g' = g * [R / (3R/2)]².

• This simplifies to g' = g * (2/3)².

• Calculating the final value: g' = g * (4/9).