Question

The gravitational force between the object is 190N. At what distance should the objects be kept so that
the force between these objects becomes 380N​

Answer 1

Answer:

Given:

Gravitational force between 2 objects = 190 N

To find:

Distance at which the objects should be kept such that Force becomes 380 N

Calculation :

Let initial distance be "d".

So initial force :

$f1 = \frac{G(m1)(m2)}{ {d}^{2} } = 190 \: newtons$

Let new distance be "d2"

So new force :

$f2 = \frac{G(m1)(m2)}{ {(d2)}^{2} } = 380 \: newtons$

Dividing the forces :

$\frac{f2}{f1} = \frac{380}{190}$

$= > \frac{ {d}^{2} }{ {(d2)}^{2} } = 2$

$= > d2 = \frac{d}{ \sqrt{2} }$

So the distance has to be (1/√2) of its initial value for the force to be 380 N.

Final answer:

$\boxed{ \huge{ \red{ d2 = \frac{d}{ \sqrt{2} }}}}$

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\small{\underline{\blue{\sf{Given :}}}}$

Distance of objects is 190 N .

Now the force became 380 N, Find distance

$\rule{200}{1}$

$\small{\underline{\green{\sf{Solution :}}}}$

We have formula for gravitational force

$\large \star {\boxed{\sf{g \: = \: G \dfrac{(m_1)(m_2)}{d^2}}}}$

Now for 1 st case

${\boxed{\sf{190 \: = \: \dfrac{G(m_1)(m_2)}{(d_1)^2}---(1)}}}$

And if Gravitational force changes to 380 N

${\boxed{\sf{380 \: = \: \dfrac{G(m_1)(m_2)}{(d_2)^2}----(2)}}}$

Divide equation (2) by (1)

$\large \implies {\sf{\dfrac{ 380 \: = \: \dfrac{G(m_1)(m_2)}{(d_1)^2} }{190 \: = \: \dfrac{G(m_1)(m_2)}{(d_2)^2} }}}$

$\implies {\sf{\dfrac{380}{190} \: = \: \dfrac{(d_1)^2}{(d_2)^2}}}$

$\implies {\sf{2 \: = \: \dfrac{(d_1)^2}{(d_2)^2}}}$

$\implies {\sf{2 \: = \: \bigg( \dfrac{d_1}{d_2} \bigg) ^2}}$

$\implies {\sf{\sqrt{2} \: = \: \dfrac{d_1}{d_2}}}$

$\implies {\sf{d_2 \: = \: \dfrac{d_1}{ \sqrt{2}}}}$

∴ Distance is 1/√2 times before