Physics - Gravitation Question with Solution | TestHub

At an altitude$\mathrm{h}$the acceleration due to gravity is

${\mathrm{g}}^{\mathrm{\prime }}=\mathrm{g}\left(1-\frac{2\mathrm{h}}{{\mathrm{R}}_{\mathrm{e}}}\right)$

$\mathrm{or} {\mathrm{mg}}^{\mathrm{\prime }}=\mathrm{mg}\left(1-\frac{2\mathrm{h}}{{\mathrm{R}}_{\mathrm{e}}}\right)$

$\mathrm{ie}, \mathrm{ }{\mathrm{w}}^{\mathrm{\prime }}=\mathrm{w}\left(1-\frac{2\mathrm{h}}{{\mathrm{R}}_{\mathrm{e}}}\right)$

$\frac{99}{100}\mathrm{w}=\mathrm{w}\left(1-\frac{2\mathrm{h}}{{\mathrm{R}}_{\mathrm{e}}}\right)$

$\mathrm{ie}, \mathrm{h}=0.005{\mathrm{R}}_{\mathrm{e}}$

At a point below the surface of the earth at depth$\mathrm{h}$. The weight of the body given by

$\mathrm{ }{\mathrm{w}}^{\mathrm{\prime }}=\mathrm{w}\left(1-\frac{\mathrm{h}}{{\mathrm{R}}_{\mathrm{e}}}\right)$

$\frac{{\mathrm{w}}^{\mathrm{\prime }}}{\mathrm{w}}=0.995$

$\mathrm{\%}∆\mathrm{w}=\frac{\left(1-0.995\right)\mathrm{w}}{\mathrm{w}}\times 100$

$\mathrm{\%}∆\mathrm{w}=0.5\mathrm{\%}$, decrease