Question

at what height the accelration due to gravity is 25% of that at the surface of the earth, the terms of radius of the earth. ​

Answer 1

To find :

Height (h) at which acceleration due to gravity(g) will be 25% of that at the surface of the Earth.

Solution :

Let the acceleration due to gravity at the surface of the earth be g₀.

We know that, acceleration due to gravity at the surface of the earth is given by :

       g₀ =                                        

     where G is the universal gravitational constant, M is the mass of the Earth and R is the radius of the Earth.

Acceleration due to gravity at a height h above the earth's surface is given by :

       

As per the given condition, g is 25% of g₀.

∴ g = 0.25 ×g₀

∴  

∴  

∴  

∴  

∴  

Answer : The acceleration due to Gravity will be 25% of that at the surface of the Earth at height of R.