Question

the gravitational force of attraction between two objects is 64 N. If the masses of both the objects are doubled without changing the distance between them, calculate the new force of attraction between the two objects​

Answer 1

Answer :

the new force of attraction between the two objects is 256 N

Explanation :

Given,

• the gravitational force of attraction between two objects is 64 N

To find,

• The new force of attraction between the two objects if the masses of both the objects are doubled without changing the distance between them

Solution,

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we know,

Gravitational force of attraction is given by,

    $\boxed {\sf \bf F=\dfrac{Gm_1m_2}{d^2}}$

where

G is the Gravitational constant ( 6.67 × 10⁻¹¹ Nm²/kg² )

m₁ is the mass of object 1

m₂ is the mass of object 2

d is the distance between the two objects

the gravitational force of attraction between two objects is 64 N

  i.e.,  $\sf 64=\dfrac{Gm_1m_2}{d^2} \: \longrightarrow [1]$

Now,

➙ masses of both the objects are doubled.

 m₁' = 2m₁

 m₂' = 2m₂

➙ distance between the objects is same

 d' = d

The new force of attraction between the two objects is

        $\sf F' = \dfrac{Gm_1'm_2'}{d' ^2} \\\\ F'=\dfrac{G(2m_1)(2m_2)}{d^2} \\\\ F'=\dfrac{4Gm_1m_2}{d^2} \longrightarrow [2]$

equation [1] ÷ equation [2]

    $\sf \dfrac{64}{F'} =\dfrac{\dfrac{Gm_1m_2}{d^2}}{\dfrac{4Gm_1m_2}{d^2}}} \\\\\\ \dfrac{64}{F'} =\dfrac{1}{4} \\\\\\ F'=64 \times 4 \\\\ F'=256 \ N$

Therefore,

the new force of attraction between the two objects is 256 N

   

Answer 2

$\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}$

New force of attraction = 256 N

$\red{\mid{\underline{\overline{\textbf{explanation}}}\mid}}$

Universal law of gravitation says that the force of gravitation between two bodies is directly proportional to product of their masses and inversely proportional to square of distance between them. It is denoted by the equation :

$\mapsto \: f = \frac{GMm}{ {d}^{2} }$

In this equation :

• G = Universal gravitational constant
• M = mass of first body
• m = mass of second body
• d = distance between them
• F = force of gravitation.

$\blue{\mid{\underline{\overline{\textbf{Coming to question :-}}}\mid}}$

In this question we have been given force of gravitation between two bodies is 64N , force of gravitation between bodies when masses will be doubled and distance will not change is not known, we have to calculate it.

Now, if force of gravitation between bodies is 64N, thus we can say.

$64n = \frac{GMm}{ {d}^{2} } \mapsto1$

Now in the asked case when masses are doubled and distance is not changed then, force of gravitation will be :

$f = \frac{G2M2m}{ {d}^{2} } \mapsto2$

Now if we find ratio of both forces we get

$\frac{64n}{f} = \frac{ \frac{GMm}{\cancel {d}^{2} } }{ \frac{G2M2m}{\cancel {d}^{2} } } \mapsto \: eq1 \div eq2$

Therefore we get the ratio to be:

$\mapsto \: \frac{64}{f} = \frac{GMm}{G2M2m}$

$\mapsto \: \frac{64}{f} = \frac{1}{4}$

$\mapsto \: 64 \times 4 = f$

$f = 256n$

Therefore new force of gravitation is 256N.

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BY SCIVIBHANSHU

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