Question

The distance of the moon from the earth is
3.8 x 105 km. Calculate the speed of the moon
revolving around the earth. Mass of the earth
6.1 * 1024 kg and G = 6.7 x 10-11
N m2 kg-2
​

Answer 1

Answer

Mass of the earth = 6.1 x 1024 kg

and

G = 6.7 x 10- N m' kg 2.

Ans. 1.03 km s-1.

Answer 2

Given Info:-

• The distance of the moon from the earth is 3.8 x 10^5 km. Calculate the speed of the moon revolving around the earth. Mass of the earth is 6.1 x 10^24 kg and G = 6.7 x 10^ -11 Nm²/kg².

Explanation :-

We know that –

$\purple{\bigstar \; {\underline{\boxed{\bf{m \dfrac{ v²}{r} =G \times \dfrac{Mm}{r²} }}}}}$    

Here,

• m= Mass of moon
• M= Mass of earth
• Gravitational constant = G (6.7 × 10^-11 Nm²/kg²)
• r= Distance from moon to earth
• v= Velocity of moon
• F= Gravitational force

$\longrightarrow \sf v² = \dfrac{Gm}{r}$

$\longrightarrow \sf v= \sqrt{\dfrac{Gm}{r} }$

${\longrightarrow { \sf{ {v} = \sqrt{\dfrac{6.7 \times {10}^{ - 11} \times \: 6.1 \times {10}^{24} }{3.8 \times {10}^{5} } } }} }$

${\longrightarrow { \sf{ {v} = \sqrt{\dfrac{4.087 \times {10}^{14} }{3.8 \times {10}^{5} } } }} }$

$\longrightarrow \bf{\pink{\underline{\underline V =3.28×10^4 \: m/s}}}$

• Hence, the speed of the moon revolving around the earth is 3.28×10^4 m/s.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━