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Let the acceleration due to gravity be g...

Let the acceleration due to gravity be `g_(1)` at a height `h` above the earth's surface `g_(2)` at a depth `d` below the earth's surface. If `g_(1)=g_(2),h lt lt R` and `d lt lt R` then

A

d=h

B

`d=(h)/(2)`

C

`d=(h)/(4)`

D

d=2h

Text Solution

Verified by Experts

The correct Answer is:
a
Acceleration due to gravity at a height h above the earth 's surface
`g_(h)-(1-2h)/(R )`
Acceration due to gravity at a depth d below the earth surface
`g_(d)=(1-(d))/(R )`
`therefore (1-(2h))/(R )=(1-(d))/(R )`
or `(1-(2h))/(r )=(1-(d))/(R )-(d)/(R ) rarr (2h)/(R )=(d)/(R)`
`rarr d=2h`
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