Question

The acceleration due to gravity is 2.5 m/s^2 at heigth h from the surface of earth. If diameter of earth is d then the magnitude of H is equal to
[Take g = 10 m/s^2]

d
d/3
d/2
2d


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Answer 1

Answer:

The gravitational force acting on mass m on the surface of Earth is

F=  

R  

2

 

GMm

​  

 

mg=  

R  

2

 

GMm

​  

 

g=  

R  

2

 

GM

​  

 

gR  

2

=GM.............(1)

where, g is acceleration due to gravity, G is gravitational constant, M is mass of Earth and R is radius of Earth.

Now, value of g at height h is

g=  

(R+h)  

2

 

GM

​  

 

As per the problem,

2

g

​  

=  

(R+h)  

2

 

GM

​  

 

g(R+h)  

2

=2gR  

2

................from (1)

(R+h)  

2

=2R  

2

 

Taking roots from both sides, we get

R+h=  

2

​  

R

∴h=  

2

​  

R−R

∴h=(  

2

​  

−1)R

Explanation: