Question

Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.

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Answer 1

Correct question :

Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth is 6×10²⁴ kg and of the Sun is 2×10³⁰ kg. The average distance between the two is 1.5×10¹¹ m.

Given :

† Mass of Earth = 6×10²⁴ kg

† Mass of Sun = 2×10³⁰ kg

† Distance between Sun and Earth = 1.5×10¹¹ m

To find :

† Force of gravitation between the Earth and Sun.

Solution :

We know that,

$\boxed {\bf {\pink {F = G \dfrac {Mm}{d^{2}}}}} \: \: \green \bigstar$

Where,

★ F = Force of gravitation

★ G = Gravitational constant

★ M = Mass of first object

★ m = Mass of second object

★ d = Distance between the two objects

Substitute the values in the formula,

$: \implies \sf {F = 6.67 \times {10}^{ - 11} \times \dfrac {6 \times {10}^{24} \times 2 \times {10}^{30} }{{(1.5 \times 10^{11})} ^{2} }}$

$: \implies\boxed {\bf {\red {F = 3.557 \times 10^{22} N}}} \: \: \blue \bigstar \: </p><p> \: \:$

Force of gravitation between the Earth and Sun is 3.557×10²² N.

Answer 2

$\begin{gathered}{ \orange{\underbrace{{\Huge{\textsf{\textbf{\red{Answer}}}}}}}}\end{gathered}$

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$\bf{ \implies{mass \: of \: earth = 6 × 10²⁴ Kg}}$

$\bf{ \implies{mass of sun = 2 × 10 ^{30} Kg}}$

$\bf \red{distance \: between \: earth \: and \: sun = 1.5 × 10¹¹ m}$

$\bf{F = \dfrac{GMm}{r²} }$

$\bf{= 6.67 × 10^{-11} × \dfrac{6 × 10²⁴ × 2 × 10^30}{(1.5 × 10¹¹)²} }$

$\bf{= { \dfrac{6.67 \times 6 - 2}{2.25} } × 10¹³ × 10^30× 10 ^{ - 22} }$

$\bf{= 35.57 × 10²¹ N}$

$\boxed{ \bf{= 3.557 × 10²² N}}$

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