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Object A attracts object B with a gravitational force of 5 newtons from a given distance. If the distance between the two objects is reduced in half, what will be the changed force of attraction between them?

Verified Answer :

Hoodsie
  1. Since the formula for gravity is gm1m2/r^2 as distance increases(or decreases) the change in force is a square of. That. So since distance is 1/2 force is squared.
skyluke89

Answer:

20 N

Explanation:

The gravitational force between the two objects is given by:

\(F=G\frac{m_A m_B}{r^2}\)

where

G is the gravitational constant

mA and mB are the masses of the two objects

r is the separation between the two objects

In this situation, we have that the distance between the two objects is reduced in half. Let's call the new distance

\(r'=\frac{r}{2}\)

So the new gravitational force F' will be

\(F'=G\frac{m_A m_B}{r'^2}=G \frac{m_A m_B}{(\frac{r}{2})^2}=4 G \frac{m_A m_B}{r^2}=4 F\)

So, the force increases by a factor 4, therefore the new force will be

\(F'=4F=4 \cdot 5 N=20 N\)

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