Question

Example 10.1 The mass of the earth is
6 x 1024 kg and that of the moon is
7.4 x 1022 kg. If the distance between the
earth and the moon is 3.84x105 km,
calculate the force exerted by the earth on
the moon. (Take G=6.7 * 10-11 N m² kg 2)​

Answer 1

Question :-

The mass of the earth is 6 * 10^24 and the mass of the moon is 7.4 * 10^22 kg. If the distance between the earth and the moon is 3.84 * 10^5 km , Calculate the force exerted by the earth on the moon. ( Take G = 6.7 * 10^-11 N m^2 kg^- 2)

Solution :-

Given that,

Mass of the earth (m1) = 6 *10^24 kg

Mass of the moon ( m2) = 7.4 * 10^22 kg

Distance between the earth and the moon

= 3.84 * 10^5

Gravitational constant = 6.7 * 10 ^-11 Nm^2 / kg^2

Now , By using Newton law of gravitation that is :-

F = Gm1m2 / r^2

Here, F denotes Force, G denotes gravitational constant, m1 denotes mass of the earth, m2 denotes mass of the moon.

Put the values in the formula ,

F = 6.7 * 10^-11 * 6 * 10^24 * 7.4 * 10^22/ (3.84 * 10^8)^2

F = 297.48 * 10^35 / 14.8225 * 10^16

F = 20.069 * 10^19

F = 20.1 * 10^19 N

Hence, The gravitational force of attraction is 20.1 * 10^19 N

Answer 2

Mass of the earth=$M_1=6×{10}^{24}\:kg$

Mass of the moon=$M_2=7.4×{10}^{22}\:kg$

Distance between earth and moon=$r=3.84×{10}^{5}\:km$

$G=6.7×{10}^{-11}\:N{m}^{2}/{kg}^{2}$

To find : $F_{12}$

Now,

by usng newton's law of gravitation

$F=G\frac{M_1×M_2}{{r}^{2}}\\\\F_{12}=6.7×{10}^{-11}×\frac{6×{10}^{24}×7.4×{10}^{22}}{{3.84×{10}^{5}}^{2}}\\\\F_{12}=2.01×{10}^{20}\:N\\\\\\\\\\\underline{\boxed{\sf{force\:exerted\:by\:earth\:to\:moon\:is \:2.01×{10}^{20}\:N }}}$