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At what depth below the surface of the e...

At what depth below the surface of the earth, acceleration due to gravity g will be half its value 1600km above the surface of the earth

A

`4.2xx10^6m`

B

`3.19xx10^6m`

C

`1.59xx10^6m`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
According to question `(g_h)/2=g_d`
`g_h=g/((1+h/R)^2)=g/((1+1600/6400)^2)=16/25g`
`g_d=g(1-d/R)`
On putting value of `g_h` and `g_d` in eq. (i)
`16/50g=g(1-d/R)`
`rArrd=Rxx34/50=4.3xx10^6m`
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