91Ó°ÊÓ

The given data can be listed below,

The mass of the earth,$M_E=5.97×{10}^{24}\mathrm{kg}$

The mass of the person,$m=60\mathrm{kg}$

The gravitational constant,$G=6.673×{10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2$

The distance between the person and the earth is the radius of the earth,$r=6.37×{10}^6\mathrm{m}$

An attractive force that creates attraction between objects is called gravitational force. It always tries to pull masses together; it never pushes them apart.

(a)

The gravitational force on the person is given by,

$F_{\text{earth on}man}=\frac{G{M}_{E}m}{r^2}$

Here, $M_E$is the mass of the earth whose value is $5.97×{10}^{24}\mathrm{kg},G$is the constant of gravitation whose value is $6.673×{10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2,m$is the mass of the person, $r$is the distance between the earth and the person.

Substitute values in the above,

$\backslash begin\left\{aligned\right\}F\_\{\backslash text\{earthonman\left\}\right\}\&=\backslash frac\{\backslash left(6.67\backslash times10^\{-11\}\backslash mathrm\left\{Nm\right\}^\left\{2\right\}/\backslash mathrm\left\{kg\right\}^\left\{2\right\}\backslash right)\backslash left(5.97\backslash times10^\left\{24\right\}\backslash mathrm\{~kg\}\backslash right\left)\right(60\backslash mathrm\{~kg\}\left)\right\}\{\backslash left(6.37\backslash times10^\left\{6\right\}\backslash mathrm\{~m\}\backslash right)^\{2\left\}\right\}\backslash \backslash \&=588\backslash mathrm\{~N\}\backslash end\left\{aligned\right\}$

Thus, the approximate magnitude of the gravitational force on the person by the earth is$588\backslash mathrm\{~N\}.$

(b)

The magnitude of gravitational force on the earth by the person is given by,

$F_{\text{man on earth}}=\frac{G{M}_{E}m}{r^2}$

Here, $M_E$is the mass of the earth whose value is $5.97×{10}^{24}\mathrm{kg},G$is the constant of gravitation whose value is $6.673×{10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2,m$is the mass of the person, $r$is the distance between the earth and the person.

Substitute all the values in the above,

$\backslash begin\left\{aligned\right\}F\_\{\backslash text\{manonearth\left\}\right\}\&=\backslash frac\{\backslash left(6.67\backslash times10^\{-11\}\backslash mathrm\left\{Nm\right\}^\left\{2\right\}/\backslash mathrm\left\{kg\right\}^\left\{2\right\}\backslash right)\backslash left(5.97\backslash times10^\left\{24\right\}\backslash mathrm\{~kg\}\backslash right\left)\right(60\backslash mathrm\{~kg\}\left)\right\}\{\backslash left(6.37\backslash times10^\left\{6\right\}\backslash mathrm\{~m\}\backslash right)^\{2\left\}\right\}\backslash \backslash \&=588\backslash mathrm\{~N\}\backslash end\left\{aligned\right\}$

Thus, the magnitude of the gravitational force on the earth by the person is $588\mathrm{N}$.