91Ó°ÊÓ

The given data can be listed below,

The mass of the earth,$M_E=5.97×{10}^{2}4kg$,

The mass of the person,$m=60 kg$

The gravitational constant,$G=6.673×{10}^{-11} Nâ‹\dots m^2/k{g}^2$

The distance between the person and the earth is the radius of the earth,

$r=6.37×{10}^6 m$

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 $5.97×{10}^{2}4 kg$ , G is the constant of gravitation whose value is $6.673×{10}^{-11} Nâ‹\dots m^2/k{g}^2$,m is the mass of the person, r is the distance between the earth and the person.

Substitute values in the above,

localid="1658071986924" $$\begin{gathered} F_{\text{earh on man}}=\frac{\left(6.67×{10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2\right)\left(5.97×{10}^{24}\mathrm{kg}\right)(60\mathrm{kg})}{{\left(6.37×{10}^6\mathrm{m}\right)}^2} \\ =588N \end{gathered}$$

Thus, the approximate magnitude of the gravitational force on the person by the earth is $588N$

(b)

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

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

Here, $M_E$is the mass of the earth whose value is localid="1658072256414" $5.97×{10}^{24} kg$, G is the constant of gravitation whose value is $6.673×{10}^{-11} Nâ‹\dots m^2/k{g}^2$ ,m is the mass of the person, r is the distance between the earth and the person.

Substitute all the values in the above,

localid="1658072379993" $$\begin{gathered} F_{\text{man on earth}}=\frac{\left(6.67×{10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2\right)\left(5.97×{10}^{24}\mathrm{kg}\right)(60\mathrm{kg})}{{\left(6.37×{10}^6\mathrm{m}\right)}^2} \\ =588N \end{gathered}$$

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