Answer
The correct answer is:
(j) $~ -4 a_{\alpha} = a_p$
Work Step by Step
By Newton's third law, the force of repulsion exerted on each particle must be equal and opposite. Let $F$ be the magnitude of the force of repulsion exerted on each particle.
We can find the magnitude of the acceleration of the $\alpha$ particle:
$a_{\alpha} = \frac{F}{4m_p} = \frac{1}{4}\times\frac{F}{m_p}$
We can find the magnitude of the acceleration of the proton:
$a_p = \frac{F}{m_p} = 4~a_{\alpha}$
Since the force acts in opposite directions on the two particles, $a_p = -4~a_{\alpha}$
The correct answer is:
(j) $~ -4 a_{\alpha} = a_p$
