Question

The force of gravitation acting between two objects is F, what will be the new force of gravitation if the distance between the two objects is halved.

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Answer 1

Answer:

4F

Explanation:

As per the the provided information in the given question, we have :

» The force of gravitation acting between two objects is F.

We've been asked to calculate the new force of gravitation if the distance between the two objects is halved.

According to the question, the force of gravitation acting between two objects is F. Let those two objects have masses of $\bf m_1$ and $\bf m_2$ and distance between them be d. Hence, force of gravitation acting between two objects will be given by,

$\implies\sf{F=G\dfrac{m_1m_2}{d^2}}$

(G = Universal Gravitational Constant)

Now, as per the question the we have to find the new force of gravitation if the distance between the two objects is halved. So, the new distance between them is half of the distance that had been taken earlier.

$\implies\sf{F'=G\dfrac{m_1m_2}{(\frac{d}{2})^2 }}$

$\implies\sf{F'=G\dfrac{m_1m_2}{\frac{d^2}{4} }}$

$\implies\sf{F'=G \times m_1m_2 \times \dfrac{4}{d^2}}$

$\implies\sf{F'=4 \times G\dfrac{m_1m_2}{d^2}}$

$\implies\underline{\boxed{\sf{F'=4F}}}$

Therefore, the new force of gravitation if the distance between the two objects is halved is 4F.

Answer 2

Given : The Force acting between two objects is F .

To Find : Find the New force if distance between these two Objects is Halved .

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SolutioN :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ F = G \dfrac{ M_1 \times M_2 }{ {d}^{2} } }}}}}$

Where :

• G = Universal Gravitational Constant
• $\sf{ M_1 }$ = Mass of 1st Object
• $\sf{ M_2 }$ = Mass of 2nd Object

$\maltese$ Calculating the New Force :

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { F = G \dfrac{ M_1 \times M_2 }{ {d}^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { F = G \dfrac{ M_1 \times M_2 }{ { \bigg( \dfrac{d}{2} \bigg) }^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { F = G \dfrac{ M_1 \times M_2 }{ { \bigg( \dfrac{ {d}^{2} }{4} \bigg) } } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { 4 \times F = G \dfrac{ M_1 \times M_2 }{ {d}^{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \; \sf { 4 \times F = F } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ F = 4F }}}}} \; {\red{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ Force will Increase by 4 times if Distance between these two objects is halved .

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