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If R(E ) be the radius of Earth ,then th...

If `R_(E )` be the radius of Earth ,then the ratio between the acceleration due to gravity at a depth 'r' below and a height 'r' above the earth surface is : (Given `:rltR_( E))`

A

`1+(r)/(R_(E))-(r_(2))/(R_(E)^(2))-(r^(3))/(R_(E)^(3))`

B

`1+(r)/(R_(E))+(r_(2))/(R_(E)^(2))+(r^(3))/(R_(E)^(3))`

C

`1-(r)/(R_(E))-(r_(2))/(R_(E)^(2))-(r^(3))/(R_(E)^(3))`

D

`1+(r)/(R_(E))-(r_(2))/(R_(E)^(2))+(r^(3))/(R_(E)^(3))`

Text Solution

Verified by Experts

The correct Answer is:
A

`(g_(h))/(g_(d))=((GM)/((R_(E)+r)^(2)))/((GM)/(R_(E)^(3))(R_(E)-r))=(R_(E)^(3))/((R_(E)+r)^(2)(R_(E)-r))`
`(g_(d))/(g_(h))=((R_(E)+r)^(2)(R_(E)-r))/(R_(E)^(3))=(R_(E)^(3)-R_(E)r^(2)+rR_(E)^(2)-r^(3))/(R_(E)^(3))`
`=1-(r^(2))/(R_(E)^(2))+(r)/(R_(E))-((r)/(R_(E)))^(3)`
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