Question

The gravitational force beween two objects is 200 N. How should the distance between the objects be changed
so that the force between them becomes 100 N?​

Answer 1

Answer:

The distance between the objects should be increased by factor of √2.

Given:

• The gravitational force between two objects is 200

To find:

• The distance between the objects be changed so that the force between them becomes 100 N

Solution:

$\sf{F=\dfrac{GM_{1}M_{2}}{R^{2}}}$

Here, G is the gravitational constant.

M1 and M2 are the masses.

R is the radius.

F is the force.

$\sf{F\propto\dfrac{1}{R^{2}}}$

$\sf{F=\dfrac{k}{R^{2}}}$

If, $\sf{200=\dfrac{k}{R^{2}}}$

Dividing both sides by 2

$\sf{\therefore{100=\dfrac{k}{2R^{2}}}}$

$\sf{\therefore{100=\dfrac{k}{(\sqrt2R)^{2}}}}$

Hence, the distance between the objects should be increased by factor of √2.

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