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 x 10-11 N m² kg)
I
f​

Answer 1

Answer:

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Step-by-step explanation:

Given that,

Mass of the Earth m

1

=6×10

24

Kg

Mass of the Moon m

2

=7.4×10

22

kg

Distance between the Earth and the Moon d=3.84×10

5

km=3.84×10

8

m

Gravitational Constant G=6.7×10

−11

Nm

2

/kg

2

Now, by using Newton’s law of gravitation

F=

r

2

Gm

1

m

2

F=

(3.84×10

8

)

2

6.7×10

−11

×6×10

24

×7.4×10

22

F=

14.8225×10

16

297.48×10

35

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

$\huge \sf {\fbox{\fbox{\red{\fbox{Answer:}}}}}$

$\huge \bf{Given:-}$

$\sf {→Mass \: of \: the \: earth,m_1 = 6 \times{{10}^{24} }}$

$\sf {→Mass \: of \: the \: moon,m_2 = 7.4\times{{10}^{22} }}$

$\sf {→Distance \: between \: the \: earth \: and \: moon,r = 3.84\times{{10}^{5} }}$

$\sf {→Distance \: between \: the \: earth \: and \: moon,r = (3.84\times{{10}^{5} \times 1000)m }}$

$\sf {→Distance \: between \: the \: earth \: and \: moon,r = 3.84\times{{10}^{8}m}}$

$\huge \bf{To \: find:- }$

$\sf{⇒Force \: exerted \: to \: one \: body \: to \: another \: body.}$

$\huge \bf{Formula \: used: - }$

$\leadsto\sf{F =G \times \frac{m_1 \times m_2}{r^2} }$

$\huge \bf{Concept \: used: - }$

$\sf{Gravitational \: constant,G=6.7 \times {10}^{- 11N} N{m}^{2}k {g}^{ - 2} }$

$\huge\bf{According \: to \: Question:-}$

$\bf{F = \frac{6.7 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 7.4 \times {10}^{22}} {(3.84 \times {10}^{8} )^{2} } = 2.01 \times {10}^{20} newtons}$

$\sf\longmapsto{2.01 \times {10}^{20} newtons}$

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