Question

Compute the force of gravity on a body of
mass 80 kg lying on the surface of the earth.
Given mass of the earth 6 x 1024 kg, radius
of the earth 6.4 x 106 m and G= 6.67 X 10-11
Nm²/kg?
(Quality answer with explanation required.)​

Answer 1

$\: \: \boxed{\boxed{\bf{\mapsto \: \: CORRECT \: QUESTION}}}$

Compute the force of gravity on a body of

mass 80 kg lying on the surface of the earth ?

Given ( mass of the earth 6 × 10²⁴ kg, radius

of the earth 6.4 × 10⁶ m and G = 6.67 X 10-¹¹ Nm²/kg²)

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$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: firstly \: let's \: understand \: the \:question}}}$

According to the question, it is given that

• mass of the earth = 6 × 10²⁴ kg

• radius of the earth = 6.4 × 10⁶ m

• G = 6.7 X 10-¹¹ Nm²/kg²

And we need to Compute the force of gravity on a body of mass 80 kg lying on the surface of the earth

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$\: \: \boxed{\boxed{\bf{\mapsto \: \: \: Solution}}}$

Given,

$\begin{gathered}\\\;\sf{\odot\;\;Gravitational \: constant\;=\;\bf{G\;=\;\bf{\orange{6.67 \times {10}^{ - 11} \: Nm ^{2} kg ^{ - 2} }}}}\end{gathered}$

$\begin{gathered}\\\;\sf{\odot\;\;Mass \: of \: earth\;=\;\bf{M\;=\;\bf{\orange{6 \times {10}^{ 24} \: kg }}}}\end{gathered}$

$\begin{gathered}\\\;\sf{\odot\;\;Mass \: of \: body\;=\;\bf{m\;=\;\bf{\orange{80\: kg }}}}\end{gathered}$

$\begin{gathered}\\\;\sf{\odot\;\;radius \: of \: earth\;=\;\bf{r\;=\;\bf{\orange{6.4 \times {10}^{6} \: kg }}}}\end{gathered}$

To find ,

$\begin{gathered}\\\;\sf{\odot\;\;gravitational \: force = \bf{\;\bf{\orange{f }}}}\end{gathered}$

~Now we know that ,

$\longrightarrow \sf F = \dfrac{GMm}{ {r}^{2} }$

⠀

$\sf \Longrightarrow F = \dfrac{6.67 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 80}{ ({6.4} \times 10^{6}) ^{2} }$

⠀

$\sf \Longrightarrow F = \dfrac{6.67 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 80}{ 6.4 \times {6.4} \times 10^{12} }$

⠀

★ Now , 10 ²⁴ - ¹¹ = 10¹³

⠀

$\sf \Longrightarrow F = \dfrac{6.67 \times 6 \times 8 \times {10}^{14} }{ 6.4 \times {6.4} \times 10^{12} }$

⠀

★ Now , 10 ¹⁴ - ¹² = 10²

⠀

$\sf \Longrightarrow F = 7.8164 \times {10}^{2}$

⠀

$\sf \Longrightarrow F = 781.64 \: N$

⠀

$\begin{gathered}\begin{gathered}\begin{gathered}\\\;\underline{\boxed{\tt{\odot\;\;Hence,\;\; force\;=\;\bf{\blue{781.64 \: N}}}}}\end{gathered} \end{gathered}\end{gathered}$

Answer 2

Given:-

→ Mass of the 1st body = 80kg

→ Mass of earth = 6×10²⁴ kg

→ Radius of Earth = 6.4×10⁶ m

→ Value of 'G' = 6.67×10⁻¹¹ Nm²/kg²

To find:-

→ Force of gravity acting on the body.

Solution:-

Here since the 1st body lying on the surface of earth, thus we will take the mass of the Earth as mass of the 2nd body. Also,we will take the radius of the earth as the distance bewteen the two bodies.

By Newton's Universal Law of Gravitation, we know that :-

F = GMm/r²

Where :-

• F is the force of gravity.

• G is Universal Gravitational Constant.

• M is mass of the 1st body.

• m is mass of the 2nd body.

• r is the distance bewteen the bodies.

Susbtituting values, we get :-

⇒ F = 6.67×10⁻¹¹×80×6×10²⁴/(6.4×10⁶)²

⇒ F = 6.67×80×6/40.96 × 10⁻¹¹⁺²⁴⁻¹²

⇒ F = 78.164 × 10

⇒ F = 781.64 N

Thus, the force of gravity is 781.64 N .