Where will a body weigh more, \({2}{k}{m}\) above the surface of earth or \({2}{k}{m}\) below the surface of earth ?

At height \({h}{\left(={2}{k}{m}\right)}\) above the surface of earth.

\({{g}_{{{h}}}=}{g{{\left({1}-\frac{{{2}{h}}}{{{R}}}\right)}}}={g{{\left({1}-\frac{{{2}\times{2}}}{{{R}}}\right)}}}={g{{\left({1}-\frac{{{4}}}{{{R}}}\right)}}}\)

and below the surface of earth at depth

\({d}{\left(={2}{k}{m}\right)}\)

\({{g}_{{{d}}}=}{g{{\left({1}-\frac{{{d}}}{{{R}}}\right)}}}={g{{\left({1}-\frac{{{2}}}{{{R}}}\right)}}}\)

From above, it is clear that

\({{g}_{{{d}}}\gt}{{g}_{{{h}}}}\) or \({m}{{g}_{{{d}}}\gt}{m}{{g}_{{{h}}}}\)

Hence body well weigh more at a depth \({2}{k}{m}\) below the surface of earth than \({2}{k}{m}\) above the surface of earth.

\({{g}_{{{h}}}=}{g{{\left({1}-\frac{{{2}{h}}}{{{R}}}\right)}}}={g{{\left({1}-\frac{{{2}\times{2}}}{{{R}}}\right)}}}={g{{\left({1}-\frac{{{4}}}{{{R}}}\right)}}}\)

and below the surface of earth at depth

\({d}{\left(={2}{k}{m}\right)}\)

\({{g}_{{{d}}}=}{g{{\left({1}-\frac{{{d}}}{{{R}}}\right)}}}={g{{\left({1}-\frac{{{2}}}{{{R}}}\right)}}}\)

From above, it is clear that

\({{g}_{{{d}}}\gt}{{g}_{{{h}}}}\) or \({m}{{g}_{{{d}}}\gt}{m}{{g}_{{{h}}}}\)

Hence body well weigh more at a depth \({2}{k}{m}\) below the surface of earth than \({2}{k}{m}\) above the surface of earth.

To Keep Reading This Answer, Download the App

4.6

Review from Google Play

To Keep Reading This Answer, Download the App

4.6

Review from Google Play

Correct29

Incorrect0

Still Have Question?

Load More

More Solution Recommended For You