Question

#problem
The mass of the planet jupiter is 1.9*10^27kg and that of the sun is 2*10^30kg.if the average distance b/w them is 7.8*10^11m. Find the gravitational force of the sun on jupiter?

need solution​

Answer 1

Answer :

Mass of jupiter = 1.9×10²⁷ kg

Mass of sun = 2×10³⁰ kg

Distance b/w them = 7.8×10¹¹ m

We have to find gravitational force of the sun on jupiter$.$

⧪ The magnitude of gravitational force between two point masses is directly proportional to the product of masses and inversely proportional to the square of the distance between them. This is known as Newton's law of gravitation also known as inverse square law.

• F ∝ M₁M₂/R²
• F = GM₁M₂/R²

G denotes gravitational constant.

The value of G does not depend on the nature and size of the masses.

$\circ\sf\:F = \dfrac{GM_1M_2}{R^2}$

$\circ\sf\:F = \dfrac{(6.67\times 10^{-11})(1.9\times 10^{27})(2\times 10^{30})}{(7.8\times 10^{11})^2}$

$\circ\sf\:F=\dfrac{25.34\times 10^{46}}{60.84\times 10^{22}}$

$\circ\sf\:F=0.416\times 10^{24}$

$\circ\:\boxed{\bf{ \purple {F=4.16\times 10^{23}\:N}}}$

The law of gravitation is universally valid. It applies to small objects on the earth, planets in the solar system and to galaxies.

Cheers!

Answer 2

Answer :

To Find :-

The Force exerted on the Planet Jupiter by the Sun.

Given :-

• Mass of Jupiter = 1.9 × 10²⁷ kg.

• Mass of sun = 2 × 10³⁰ kg.

• Distance between Jupiter and Sun = 7.8 × 10¹¹ m.

We know :-

⠀⠀⠀⠀⠀Force of Gravitation :-

$\boxed{\underline{\bf{F = G\dfrac{m_{1}m_{2}}{r^{2}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀Where :-

⠀⠀⠀$G$ = Universal Gravitational constant

⠀⠀⠀$m_{1}$ = Mass of an Planet.

⠀⠀⠀$m_{2}$ = Mass of Another Planet.

Concept :-

• Force is directly proportional to the product of the masses of two objects.

⠀⠀⠀⠀⠀⠀⠀⠀$\bf{F \propto m_{1}m_{2}}$

• Force is inversely proportional to the square of Distance between the two objects.

⠀⠀⠀⠀⠀⠀⠀⠀$\bf{F \propto \dfrac{1}{r^{2}}}$

• The constant in the Force of gravitation is G. The value of G is 6.67 × 10-¹¹ N m²/kg².

Solution :-

Given :

• $m_{1}$ = 1.9 × 10²⁷ kg.
• $m_{2}$ = 2 × 10³⁰ kg.
• $r$ = 7.8 × 10¹¹ m.
• $G$ = 6.67 × 10-¹¹ N m²/kg².

Using the formula and substituting the values in it , we get :-

$:\implies \bf{F = G\dfrac{m_{1}m_{2}}{r^{2}}} \\ \\ \\ \\ :\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{1.9 \times 10^{27} \times 2 \times 10^{30}}{(7.8 \times 10^{11})^{2}}\bigg)} \\ \\ \\ \\ :\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{1.9 \times 10^{27} \times 2 \times 10^{30}}{(7.8 \times 10^{11})(7.8 \times 10^{11})}\bigg)}$

$:\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{1.9 \times 10^{27} \times 2 \times 10^{30}}{7.8 \times 7.8 \times 10^{11} \times 10^{11}}\bigg)} \\ \\ \\ \\ :\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{1.9 \times 10^{27} \times 2 \times 10^{30}}{7.8 \times 7.8 \times 10^{22}}\bigg)}$

$:\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{3.8 \times 10^{27} \times 10^{30}}{60.84 \times 10^{22}}\bigg)} \\ \\ \\ \\ :\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{3.8 \times 10^{57}}{60.84 \times 10^{22}}\bigg)}$

$:\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{3.8 \times 10^{57} \times 10^{-22}}{60.84}\bigg)} \\ \\ \\ \\ :\implies \bf{F = 6.67 \times 10^{-11} \times \bigg(\dfrac{3.8 \times 10^{35}}{60.84}\bigg)}$

$:\implies \bf{F = \dfrac{6.67 \times 10^{-11} \times 3.8 \times 10^{35}}{60.84}} \\ \\ \\ \\ :\implies \bf{F = \dfrac{25.346 \times 10^{24}}{60.84}} \\ \\ \\ \\ :\implies \bf{F = 0.42 \times 10^{24}} \\ \\ \\ \\ :\implies \bf{F = 4.2 \times 10^{23}} \\ \\ \\ \\ \therefore \purple{\bf{F = 4.2 \times 10^{23} N}}$

Hence, the force exerted on the planet Jupiter by the Sun is 4.2 × 10²³ N.