Science, asked by vedantkunghatkar777, 6 months ago

Find the odd one out:
(1)
Change in value of 'g' at surface, change in value of 'g' at height, change in value
of 'g' at depth, change in value of 'g' on thickness.

if the answer will be correct then i will follow you and also mark you as brainliest.​

Answers

Answered by mahekchabriya7093
1

Answer:

Let, g  

h

​  

 be the acceleration due to gravity at height h.

g  

x

​  

 be the acceleration due to gravity at depth x.

The acceleration due to gravity on the surface of Earth is

g=  

R  

2

 

GM

​  

 

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

∴g∝  

R  

2

 

1

​  

 

⇒g  

h

​  

∝  

(R+h)  

2

 

1

​  

 

Therefore

g

g  

h

​  

 

​  

=  

(R+h)  

2

 

R  

2

 

​  

 

g

g  

h

​  

 

​  

=  

(1+  

R

h

​  

)  

2

 

1

​  

 

g

g  

h

​  

 

​  

=(1+  

R

h

​  

)  

−2

 

g

g  

h

​  

 

​  

=(1−  

R

2h

​  

)

g  

h

​  

=g−  

R

2gh

​  

 

g−g  

h

​  

=  

R

2gh

​  

 

Also, the acceleration due to gravity at depth x,

g  

x

​  

=  

3

4

​  

Gρ(R−x)

⇒g  

x

​  

∝(R−x)

Therefore

g

g  

x

​  

 

​  

=  

R

R−x

​  

 

g

g  

x

​  

 

​  

=1−  

R

x

​  

 

g  

x

​  

=g−  

R

gx

​  

 

g−g  

x

​  

=  

R

gx

​  

 

If the change in the value of g at height h above earth surface is the same as that at depth x i.e.

g−g  

h

​  

=g−g  

x

​  

 

R

2gh

​  

=  

R

gx

​  

 

∴x=2h

Explanation:

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