Question

The mass of the earth is 6 x $10^24$ kg and the moon is 7.4 x$10^{22}$kg .If the distance between the earth and the moon is 3.84x10$^5$km ,calculate the force exerted by the earth on the moon.Take G = 6.7x10$^{-11}Nm^{2}kg^{-2}$

Answer 1

Answer:

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Explanation:

We know the force of attraction between two object is given by the formulaF=

R

2

GMm

=

(3.84×10

8

)

2

6.7×10

−11

×6×10

24

×7.4×10

22

=2.0×10

20

N

Answer 2

Correct Question :-

The mass of the earth is 6 × 10^24kg and that of the moon is 7.4 × 10^22kg. If the distance between the earth and the moon is 3.84 × 10^5km, calculate the force exerted by the earth on the moon.Take G = 6.7 × 10^-11N

m^2kg^-2

Answer :-

2.01 × 10^20 N.

Explanation :-

Formula require:

$\sf{F=G\dfrac{M\times m}{d^2}$

Solution:

$\sf{}F=G\dfrac{M\times m}{d^2}\\ \\ \\ \sf{}\Rightarrow \dfrac{6.7\times 10^{-11}\times6\times10^{24}\times 7.4\times10^{22}}{(3.84\times10^8)^2}\\ \\ \\ \Rightarrow \dfrac{297.48\times10^{8-11+24+22}}{3.84\times10^8 \times 3.84\times10^8}\\ \\ \\ \Rightarrow \dfrac{297.48\times10^{35}}{14.74\times10^{16}}\\ \\ \\ \Rightarrow 20.18\times10^{35-16}\\ \\ \\ \Rightarrow 20.18\times10^{19}\\ \\ \\ \Rightarrow 20.18\times10^{19}\times \dfrac{10}{10}\\ \\ \\ \Rightarrow 2.01\times10^{19+1}$

$\therefore \sf{2.01\times10^{20}}$

Thus,the force exerted by the earth on the moon is 2.01 × 10^20 N