Question

derive an expression variation of acceleration due to gravity with their height​

Answer 1

Answer:

For an object placed at a height h, the acceleration due to gravity is less as compared to that placed on the surface. As depth increases, the value of acceleration due to gravity (g) falls. The value of g is more at equator and less at poles

Explanation:

let we consider,

radius of earth R and mass is M  

and we know that acceleration due to gravity at surface  

g=  

R  

2

 

GM

​  

  ----   (i)

G is universal gravitational constant.  

consider, a mass m is at above the earth at height h and g  

′

 is acceleration due to gravity at height h.

Therefore,

​  divide, (ii) by (i)

g

g  

′

 

​  

=  

(R+h)  

2

 

R  

2

 

​  

 

g  

′

=  

(R+h)  

2

 

gR  

2

 

​  

 

For h<<<R,  

g  

′

=g(1−  R 2h  )