volume_mute
Two objects move to be closer
publish date: 2024/03/22 20:24:6.544086 UTC
volume_muteSuppose two objects are initially 5 meters apart and then are moved to 1 meter apart. How does the force of gravity between them change?
It becomes 25 times greater
It becomes 1 times greater
It becomes 24 times greater
Correct Answer
It becomes 25 times greater
Explanation
If the distance between two objects decreases from 5 meters to 1 meter, the force of gravity between them will increase significantly.
To quantify this change, we can use the inverse square law formula for gravitational force:
$F \sim \dfrac{m_1 \cdot m_2}{d^2}$
Since the masses of the objects remain constant, the change in force (ΔF) is inversely proportional to the square of the change in distance (Δd):
ΔF ∝ \(\dfrac{1}{(Δd)}\)
So, if the distance decreases from 5 meters to 1 meter (Δd =5−1= 4 meters), the force of gravity will increase by a factor of:
\(\frac{1^2}{\frac{1}{5^2}} = \frac{5^2}{1^2} = 25\)
Therefore, the force of gravity will increase by a factor of 25 times when the distance between the two objects decreases from 5 meters to 1 meter.
Reference
Basic Physics: A Self-Teaching Guide