The new acceleration is B) 4a
Explanation:
According to Newton's second law, the acceleration of an object is proportional to the force exerted on it:
where
F is the net force on the object
m is its mass
a is the acceleration
This means that we can analyze the problem in terms of the force involved. The electric force between the charges at the beginning is given by
where:
is the Coulomb's constant
are the two charges
D is the separation between the two charges
Later, the charges are separated by a new distance
D' = D/2
Therefore, the new force between them is
So, the force has increased by a factor of 4: and since the acceleration is proportional to the force, this means that the acceleration has also increased by a factor of 4, so the correct choice is
B) 4a
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