Question

The masses of the earth and moon
are 6 x 10 kg and 7.4x10 kg
respectively. The distance between
them is 3.84 x 10m Calculate the
gravitational force of attraction
between the two
Use G = 6.7 x 10" N m'kg
please answer me​

Answer 1

Question :-

The masses of the earth and moon are 6 x 10²⁴ kg and 7.4 x 10²² kg . If the distance between them is 3.84 x 10^5 km . Calculate the gravitational force of attraction between the two . use G = 6.67 x 10^-11 N m² kg^-2 .

Given :-

Mass of the earth ( M ) = 6 x 10²⁴ kg

Mass of the moon ( m ) = 7.4 x 10²² kg

Distance between the earth and the moon = 3.84 x 10^5 metres

Required to find :-

• Gravitational force of attraction between the earth and the moon

Formulae used :-

$\boxed{\huge{\mathsf{Force \; of \; attraction = \dfrac{ G \; M \; m }{ d^2 }}}}$

where,

G = Gravitational constant

M & m = Masses of the bodies

d = Distance between them

Solution :-

Mass of the earth ( M ) = 6 x 10²⁴ kg

Mass of the moon ( m ) = 7.4 x 10²² kg

Distance between the earth and the moon ( d ) = 3.84 x 10^5 meters

G = 6.67 x 10^-11 N m² kg ^-2

We know that,

$\mathsf{ Force \; of \; attraction = \dfrac{ G \; M \; m }{ {d}^{2}}}$

So, substitute the given values ,

$\tt{F = \dfrac{6.67 \times {10}^{-11} N m^2 {kg}^{-2} \times 6 \times {10}^{24} \times 7.4 \times {10}^{22} }{(3.84 \times 10^8{)}^{2}}}$

Now let's ignore the units in order to simplify our calculations .

$\tt{ F = \dfrac{6.67 \times 6 \times 7.4 \times {10}^{-11} \times {10}^{24} \times {10}^{22}}{3.84 \times 10^8 \times 3.84 \times 10^8}}$

$\tt{ F = \dfrac{6.67 \times 6 \times 7.4 \times {10}^{-11} \times {10}^{24 + 22}}{3.84 \times 10^8 \times 3.84 \times 10^8 }}$

$\tt{ F = \dfrac{6.67 \times 6 \times 7.4 \times {10}^{-11} \times {10}^{46}}{3.84 \times 10^8 \times 3.84 \times 10^8 }}$

$\tt{ F = \dfrac{ 6.67 \times 6 \times 7.4 \times { 10}^{-11 + 46}}{3.84 \times 3.84 \times {10}^{8 + 8}}}$

$\tt{ F = \dfrac{ 6.67 \times 6 \times 7.4 \times {10}^{35}}{3.84 \times 3.84 \times {10}^{16} }}$

$\tt{ F = \dfrac{ 6.67 \times 6 \times 7.4 \times {10}^{35}}{14.7456}}$

$\tt{ F = \dfrac{ 296.148 \times {10}^{35 - 16}}{14.7456}}$

$\tt{ F = \dfrac{ 296.148 \times {10}^{19}}{14.7456}}$

Now multiply both numerator and denominator with 10000

So,

$\tt{ F = \dfrac{ 296.148 \times {10}^{19} \times 10000}{14.7456 \times 10000}}$

$\tt{ F = \dfrac{ 296.148 \times 1000 \times {10}^{19} \times 10^1 }{147456}}$

$\tt{ F = \dfrac{ 296148 \times {10}^{19 + 1}}{147456}}$

$\tt{ F = \dfrac{ 296148 \times {10}^{20}}{147456}}$

By reducing we get,

$\tt{ F = \dfrac{ 370185 \times {10}^{20} }{36864}}$

On simplifying further we get ,

$\red{\implies{\underline{\large{\tt{ 2.01 \times {10}^{20} N}}}}}$

Therefore,

The gravitational force of attraction between the earth and the moon is 2.01 x 10^20 N .

Points to remember :-

1. If the mass increases then the force of attraction between them will also increase and vice-versa
2. If the distance between them increases then the force of attraction between them will decrease and vice-versa
3. The above formula was derived from the Universal Law of Gravitation .

Universal Law of Gravitation :-

" In the universe every object attracts every other object with some force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them "

Answer 2

Answer:

Question :-

The masses of the earth and moon are 6 x 10²⁴ kg and 7.4 x 10²² kg . If the distance between them is 3.84 x 10^5 km . Calculate the gravitational force of attraction between the two . use G = 6.67 x 10^-11 N m² kg^-2 .

Given :-

Mass of the earth ( M ) = 6 x 10²⁴ kg

Mass of the moon ( m ) = 7.4 x 10²² kg

Distance between the earth and the moon = 3.84 x 10^5 metres

Required to find :-

Gravitational force of attraction between the earth and the moon

Formulae used :-

\boxed{\huge{\mathsf{Force \; of \; attraction = \dfrac{ G \; M \; m }{ d^2 }}}}

Forceofattraction=

d

2

GMm

where,

G = Gravitational constant

M & m = Masses of the bodies

d = Distance between them

Solution :-

Mass of the earth ( M ) = 6 x 10²⁴ kg

Mass of the moon ( m ) = 7.4 x 10²² kg

Distance between the earth and the moon ( d ) = 3.84 x 10^5 meters

G = 6.67 x 10^-11 N m² kg ^-2

We know that,

\mathsf{ Force \; of \; attraction = \dfrac{ G \; M \; m }{ {d}^{2}}}Forceofattraction=

d

2

GMm

So, substitute the given values ,

\tt{F = \dfrac{6.67 \times {10}^{-11} N m^2 {kg}^{-2} \times 6 \times {10}^{24} \times 7.4 \times {10}^{22} }{(3.84 \times 10^8{)}^{2}}}F=

(3.84×10

8

)

2

6.67×10

−11

Nm

2

kg

−2

×6×10

24

×7.4×10

22

Now let's ignore the units in order to simplify our calculations .

\tt{ F = \dfrac{6.67 \times 6 \times 7.4 \times {10}^{-11} \times {10}^{24} \times {10}^{22}}{3.84 \times 10^8 \times 3.84 \times 10^8}}F=

3.84×10

8

×3.84×10

8

6.67×6×7.4×10

−11

×10

24

×10

22

\tt{ F = \dfrac{6.67 \times 6 \times 7.4 \times {10}^{-11} \times {10}^{24 + 22}}{3.84 \times 10^8 \times 3.84 \times 10^8 }}F=

3.84×10

8

×3.84×10

8

6.67×6×7.4×10

−11

×10

24+22

\tt{ F = \dfrac{6.67 \times 6 \times 7.4 \times {10}^{-11} \times {10}^{46}}{3.84 \times 10^8 \times 3.84 \times 10^8 }}F=

3.84×10

8

×3.84×10

8

6.67×6×7.4×10

−11

×10

46

\tt{ F = \dfrac{ 6.67 \times 6 \times 7.4 \times { 10}^{-11 + 46}}{3.84 \times 3.84 \times {10}^{8 + 8}}}F=

3.84×3.84×10

8+8

6.67×6×7.4×10

−11+46

\tt{ F = \dfrac{ 6.67 \times 6 \times 7.4 \times {10}^{35}}{3.84 \times 3.84 \times {10}^{16} }}F=

3.84×3.84×10

16

6.67×6×7.4×10

35

\tt{ F = \dfrac{ 6.67 \times 6 \times 7.4 \times {10}^{35}}{14.7456}}F=

14.7456

6.67×6×7.4×10

35

\tt{ F = \dfrac{ 296.148 \times {10}^{35 - 16}}{14.7456}}F=

14.7456

296.148×10

35−16

\tt{ F = \dfrac{ 296.148 \times {10}^{19}}{14.7456}}F=

14.7456

296.148×10

19

Now multiply both numerator and denominator with 10000

So,

\tt{ F = \dfrac{ 296.148 \times {10}^{19} \times 10000}{14.7456 \times 10000}}F=

14.7456×10000

296.148×10

19

×10000

\tt{ F = \dfrac{ 296.148 \times 1000 \times {10}^{19} \times 10^1 }{147456}}F=

147456

296.148×1000×10

19

×10

1

\tt{ F = \dfrac{ 296148 \times {10}^{19 + 1}}{147456}}F=

147456

296148×10

19+1

\tt{ F = \dfrac{ 296148 \times {10}^{20}}{147456}}F=

147456

296148×10

20

By reducing we get,

\tt{ F = \dfrac{ 370185 \times {10}^{20} }{36864}}F=

36864

370185×10

20

On simplifying further we get ,

\red{\implies{\underline{\large{\tt{ 2.01 \times {10}^{20} N}}}}}⟹

2.01×10

20

N

Therefore,

The gravitational force of attraction between the earth and the moon is 2.01 x 10^20 N .

Points to remember :-

If the mass increases then the force of attraction between them will also increase and vice-versa

If the distance between them increases then the force of attraction between them will decrease and vice-versa

The above formula was derived from the Universal Law of Gravitation .

Universal Law of Gravitation :-

" In the universe every object attracts every other object with some force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them "