Distance of a planet from the earth is 2.5 x 107 km and the gravitational force between them is 3.82 x 1018 N. Mass of the planet and earth are equal, each being 5.98 x 1024 kg. Calculate the universal gravitation constant.
Answers
☯ Using Newton's Law Of Gravitation
Answer:
Given :
▪ Distance b/w earth and planet =
2.5×10^7
7
km
▪ Gravitational force b/w them =
3.82×10^{18}
18
N
▪ Mass of both = 5.98×10^{24}
24
kg
To Find :
▪ Universal gravitational constant
Formula :
✒ Newton's law of Gravitation,
\bigstar\:\underline{\boxed{\bf{\pink{F=\dfrac{Gm_1m_2}{r^2}}}}}★
F=
r
2
Gm
1
m
2
Calculation :
\begin{gathered}:\implies\sf\:3.82\times 10^{18}=\dfrac{G\times (5.98\times 10^{24})^2}{(2.5\times 10^9)^2}\\ \\ :\implies\sf\:3.82\times 10^{18}=\dfrac{G\times 35.76\times 10^{48}}{6.25\times 10^{18}}\\ \\ :\implies\sf\:G=\dfrac{3.82\times 10^{18}\times 6.25\times 10^{18}}{35.76\times 10^{48}}\\ \\ \longrightarrow\underline{\boxed{\bf{\purple{G=6.67\times 10^{-11}\:Nm^2kg^{-2}}}}}\end{gathered}
:⟹3.82×10
18
=
(2.5×10
9
)
2
G×(5.98×10
24
)
2
:⟹3.82×10
18
=
6.25×10
18
G×35.76×10
48
:⟹G=
35.76×10
48
3.82×10
18
×6.25×10
18
⟶
G=6.67×10
−11
Nm
2
kg
−2
____________________________
✴ Extra Dose :
The value of G does not depend on the nature and size of the masses.
The law of gravitation is universally valid. It applies to small objects on the earth, planets in the solar system and to galaxies