The electric force between two charged objects can be described by Coulomb's Law, which states that the force \( F \) between two charges is inversely proportional to the square of the distance \( r \) between them:
\[ F \propto \frac{1}{r^2} \]
If the original force is \( F_1 = 0.24 \) newtons and the distance is increased by a factor of 4, the new distance \( r' \) will be:
\[ r' = 4r \]
The new force \( F_2 \) can be calculated as:
\[ F_2 = \frac{F_1}{(k^2)} \]
where \( k \) is the factor by which the distance is increased. In this case, \( k = 4 \).
Thus,
\[ F_2 = \frac{0.24 , \text{N}}{(4^2)} = \frac{0.24 , \text{N}}{16} = 0.015 , \text{N} \]
So the new force is 0.015 newtons.
The correct answer is A. 0.015 newtons.