## College Physics (4th Edition)

The correct answer is: (j) $~ -4 a_{\alpha} = a_p$
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) $~ -4 a_{\alpha} = a_p$