Physics - Gravitation Question with Solution | TestHub

$\text{Given h}=\frac{R_e}{2}$

Acceleration due to gravity at altitude h is given by

${\text{g}}^{\prime }=\frac{\text{g}}{{\left(1+\frac{h}{R_e}\right)}^2}$

$=\frac{\text{g}}{{\left(1+\frac{R_e/2}{R_e}\right)}^2}$

$=\frac{\text{g}}{{\left(1+\frac{1}{2}\right)}^2}$

$=\frac{\text{g}}{{\left(3/2\right)}^2}=\text{g'}=\frac{4}{9}\text{ g}$...(i)

Weight of the body at earth's surface

$w=mg=63 \mathrm{N}$...(ii)

Weight of the body at altitude$h=\raisebox{1ex}{$R_e$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

$w^{\prime }=\text{m}{g}^{\prime }=\frac{4}{9}\text{mg}$...(iii)

Using Eq. (ii), we get

$w^{\prime }=\frac{4}{9}\times 63$

$w\text{'}=28 \mathrm{N}$