Question

if distance between two bodies is increased by 25%, then the % change in
gravitational force
(a) Decreases by 36%
(b) Increases by 36%
(c) Increases by 64%
(d) Decreases by 64%​

Answer 1

The % change in gravitational force is decreases by 36%.

Option - A

Explanation:

We know that,

The formula of force of gravity, F =  $\frac{Gm_1m_2}{d^2}$

Where is theG is the Gravitational constant.

$m_1$ and $m_2$ is the masses of the two bodies 1 and 2 respectively.

d is the distance of the of the two bodies.

Then,

If the the distance between two bodies is increased by 25%,

So,

d' is the distance of the of the two bodies after the distance increased by 25%,

                         d' = d + $\frac{25}{100} \times d$

                             = d + $\frac{1d}{4}$

                             = $\frac{5d}{4}$

Then,

The force of gravity after the distance increased by 25%, F' = $\frac{Gm_1m_2}{d'^2}$

                         F' =$\frac{Gm_1m_2}{d'^2}$

                            = $\frac{Gm_1m_2}{\frac{5d}{4}^2}$

                             = $\frac{16}{25}$ $\frac{Gm_1m_2}{d^2}$

                          F'= $\frac{16}{25}$ F

The change in  gravitational force $\Delta F$(%) = $\frac{F' - F}{F} \times 100$

                             = $\frac{\frac{16}{25} F - F}{F} \times 100$

                             = $(\frac{16}{25} - 1 ) \times 100$

                             = $\frac{16 - 25}{25} \times 100$

                             = (-9) $\times$ 4

                      $\Delta F$ = -36%

Here, the (-) negative sign indicates the decreasing of the gravitational force.

Hence, the % change in gravitational force is decreases by 36%.

To know more:

How does the force of gravitation between two objects change when the distance between them is doubled

https://brainly.in/question/4223820

Answer 2

Answer:

gigb ug glad that you are definitelyCorrect option is

A

Decreases by 36%

F=

r

2

Gm

1

m

2

r

′

=r+

4

r

F

′

=

25

16F

F

′

=64%F

Thus, the force decreases by 36%