Question

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?
A. 2.5 newtons
B. 10 newtons
C.15 newtons
D. 20 newtons
E. 25 newtons

Answer 1

The new force of gravitational attraction is D. 20 newtons

Explanation:

The magnitude of the gravitational force between two objects is given by :

$F=G\frac{m_1 m_2}{r^2}$  (1)

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m1, m2 are the masses of the two objects

r is the distance between them

In this problem, the initial gravitational force between the two objects A and B is

F = 5 N

When the distance between them is r.

Later, the distance is reduced in half:

$r' = \frac{r}{2}$

Substituting into eq.(1), we see how does the  force change:

$F' = G\frac{m_1 m_2}{r'^2}=G\frac{m_1 m_2}{(r/2)^2}= 4 (G\frac{m_1 m_2}{r^2})=4F$

So, the force increases by 4 times. Therefore, the new force is

$F'=4F=4(5 N) = 20 N$

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