Answer
$4.9\times 10^{-7}\ kg$
Work Step by Step
It is given that:
acceleration of the first particle $a_1 = 7\ m/s^2 $
acceleration of the second particle $a_2 = 9\ m/s^2 $
mass of first particle $m_1=6.3\times 10^-7\ kg$
let $m_2$ be the mass of the second particle
When these two particles are separated by a distance, then the magnetic force acting on the first particle due to the second particle is equal to magnetic force acting on the second particle due to first particle.
So,
$F_1 = F_2$
$m_1 a_1 = m_2 a_2$
$m_2 = \frac{m_1 a_1}{a_2}$
$m_2 = \frac{(6.3\times 10^{-7})(7\ m/s^2)}{9\ m/s^2} = 4.9\times 10^{-7}\ kg$
