Question

The masses of the earth and moon
are 6 x 1024 kg and 7.4x1022. kg,
respectively. The distance between
them is 3.84 x 109 km. Calculate the
gravitational force of attraction
between the two?
Use G = 6.7 x 10-11 N m² kg 2​

Answer 1

Hey Pretty Stranger!

• Mass of the earth, M = 6 × 10²⁴ kg

• Mass of the moon, m = 7.4 × 10²² kg

• Distance b/w both, d = 3.84 × 10⁵ km

→ d = 3.84 × 10⁵ km

→ d = 3.84 × 10⁵ × 1000 m

→ d = 3.84 × 10⁸ m

• G = 6.7 × 10⁻¹¹ Nm² kg⁻²

From Newton's Law of Gravitation :

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

$\sf \: \longrightarrow \: \dfrac{6.7 \times {10}^{ - 11 } \times 6 \times {10}^{24} \times 7.4 \times {10}^{22} }{(3.84 \times {10}^{8}m) ^{2} }$

$\sf \: \longrightarrow \: 2.02 \times {10}^{20} \: N$

$\therefore$ The gravitational Force of attraction between the two is $\sf \: 2.02 \times {10}^{20} \: N$

Answer 2

• Mass of the earth, M = 6 × 10²⁴ kg

• Mass of the moon, m = 7.4 × 10²² kg

• Distance b/w both, d = 3.84 × 10⁵ km

→ d = 3.84 × 10⁵ km

→ d = 3.84 × 10⁵ × 1000 m

→ d = 3.84 × 10⁸ m

• G = 6.7 × 10⁻¹¹ Nm² kg⁻²

From Newton's Law of Gravitation :

\bigstar \: \sf \: F = G \: \dfrac{M \times m}{ {d}^{2} }★F=G

d

2

M×m

\sf \: \longrightarrow \: \dfrac{6.7 \times {10}^{ - 11 } \times 6 \times {10}^{24} \times 7.4 \times {10}^{22} }{(3.84 \times {10}^{8}m) ^{2} }⟶

(3.84×10

8

m)

2

6.7×10

−11

×6×10

24

×7.4×10

22

\sf \: \longrightarrow \: 2.02 \times {10}^{20} \: N⟶2.02×10

20

N

\therefore∴ The gravitational Force of attraction between the two is \sf \: 2.02 \times {10}^{20} \: N2.02×10

20

N