Question

How does the gravitational force between two object is f how will the force change when the distance between them is reduced the 1/3

Answer 1

Answer:

Explanation:

➟ The gravitational force of earth is known as gravity i.e., gravity is the force by which earth pulls a body toward it's centre.

➟ Gravitation- Every body attract other body by a force called force of gravitation.

➣ Newton's law of gravitation- The force of gravitational attraction between two points bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Considering two points ${\sf{m_{1} \: and \: m_{2}}$ are placed at a distance ${\sf{r}}$ The force of gravitational attraction between them, ${\sf{F \: = G\dfrac{m_{1}m_{2}}{r^{2}}}}$

Here ${\sf{G}}$ is constant called universal gravitational constant. The value of G is ${\sf{6.67 \times 10^{-11} Nm^{2}/kg^{2}}}$

$\setlength{\unitlength}{7mm} \begin{picture}(6,6)\thicklines\put(2,2){\circle{14}}\put(8,2){\circle{}} \put(2,2){\circle*{0.15}} \put(8,2){\circle*{0.15}} \put(2,2){\line(8,0){6}} \put(4,2){ \bf Force }{\line( - 1,1){0}} \put(6,2){\line(1,1){0.5}} \put(4,2){\line( - 1, - 1){0.5}} \put(6,2){\line( 1, -1){0.5}} \put(4.5,0.7){\vector( - 1,0){2.7}} \put(5.4,0.7){\vector(1,0){2.8}}\put(4.75,0.6){ \bf d }\put( 3.3, - 1){ \framebox{ \bf F = \displaystyle \dfrac{GMm}{d^2} }} {\pmb{\sf{BrainlyButterfliee}}}\end{picture}$

→ Let two objects A and B of masses M and m lie at a distance, d from each other.

Now let the force of attraction between then be F.

→ Now according to the universal law of gravitation, the force between two objects is directly proportional to their masses. Therefore,

→ F ∝ M × m

→ F ∝ Mm – – – Equation 1

→ And we also know that the force between two objects is inversely proportional to the square of the distance between them. Therefore,

→ F ∝ 1/(d)² – – – Equation 2

→ From – – – Equation 1 and 2

→ F ∝ Mm/(d)²

Let's remove proportional sign, by adding constant as G here

→ F = GMm/(d)²

Henceforth,

→ G = Fd²/Mm Henceforth, derived!

______________________

Now let us solve this question!

Given that:

• The Gravitational Force between two object is “F”.

• The distance between them is reduced to “1/3”.

To determine:

• How will the force change!?

Solution:

• The force will change to 9 times.

==> F = GMm/d²

==> F = GMm/(1/3)²

==> F = GMm/1/9

==> F = 9GMm

Therefore, the force will change 9 times when the distance between two object reduced the 1/3.