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# Calculate the distance from the surface of the earth at which the acceleration due to gravity is the same below as well as above the surface of earth.

9 years ago

gh = gs ( R/(R+H))2                                      where s is surface and h is height

gd = gs ( (R-d)R)                                       where d is depth

gh = gs

gs ( R/(R+H))2 = gs ( (R-d)R)

since H = d

therefore

(R2)R = (R -d)((R+H)2)

R3 = R3 - RH2 + HR2 - H3

H3 = H( R2 - RH )

H2 = R2 - RH

H2 + RH - R2 = 0

Substitute the value of R as 6400 km

then the answer will come as 3200(√6 -1) km.

9 years ago

Hi Arnab,

Let Re be the radius of the earth.

And let x be the distance at which the accn due to gvt is the same (both above and below)

For above,

g = gs*[ Re2/(Re+x)2 ] -----------(1)

For below

g = gs* [ (Re-x)/Re ] --------------(2)

where gs is the accn due to gvt at the surface of the earth.

Both are given to be equal. So (1) = (2) will imply,

[ Re2/(Re+x)2 ] = [ (Re-x)/Re ]

Hence x2 + Rex - Re2 = 0

Which will give x = [(√5 - 1)/2]*Re.

Considering Re to be 6400km, will yield x = 3200{√5 - 1}

Hope this helps.

Best Regards,