Question

The mass of the earth is 6 Ã 1024 kg and that of the moon is 7.4 Ã1022 kg. If the distance between the earth and the moon be 3.84 Ã 105 km, calculate the force exerted by the earth on the moon. (G = 6.7 Ã 10â11 Nm2 kgâ2â)

Answer 1

The force exerted by the earth on the moon is 2.017×$10^{22}$ (N).

Explanation:

1. Force between earth and mood is calculate from formula.

  F = $\frac{G\times M_{e}\times M_{m}}{D^{2}}$    ...a)

  Where

  G = Gravitational constant = 6.7×$10^{-11}$ $(\frac{Nm^{2}}{kg^{2}})$

  $M_{e}$ = mass of earth = 6×$10^{24}$ (kg)

  $M_{m}$ = mass of moon = 7.4×$10^{22}$ (kg)

  D= distance between earth and moon = 3.84×$10^{8}$ (m)

2. From equation a)

  F = $\frac{6.7\times 10^{-11}\times 6\times 10^{24}\times 7.4\times 10^{22}}{(3.84\times 10^{8})^{2}}$

F = $\frac{20.17\times 10^{-11}\times 10^{24}\times 10^{22}}{10^{16}}$

So force exerted by earth on moon (F) = 2.017×$10^{22}$ (N)

Answer 2

Force exerted By Earth is $2.01 \times 10^2^0$ N

Explanation:

• The Mass of Earth, M = $6 \times 10^2^4 kg$

• The Mass of Moon, m = $7.4 \times 10^2^2 kg$

The Distance between Earth as well as Moon is,

r = $3.84 \times 10^5$

= $3.84 \times 10^5 \times 1000$

= $3.84 \times 10^8 m$

The Value of $G = 6.7 \times 10^-^1^1 Nm^2kg^-^2$

• The force exerted by earth upon the moon is,  

F = $\frac {GMm}{R^2}$

= $\frac {6.7 \times 10^-^1^1 \times 6 \times 10^2^4 \times 7.4 \times 10^2^2}{(3.84 \times 10^8)^2}$

= $2.01 \times 10^2^0$ N

Hence, The Force exerted by the earth on the Moon is $2.01 \times 10^2^0 N$