Answer
The mass of the other sphere is $~~100~g$
Work Step by Step
Let $m_1 = 300~g$, let the velocity $v_{1i} = v$, and let $v_{1f} = 0$
Then: $~~v_{2i} = -v$
We can use Equation (9-75) to find the mass $m_2$ of the other sphere:
$v_{1f} = \frac{m_1-m_2}{m_1+m_2}~v_{1i}+\frac{2m_2}{m_1+m_2}~v_{2i}$
$0 = \frac{m_1-m_2}{m_1+m_2}~v+\frac{2m_2}{m_1+m_2}~(-v)$
$\frac{2m_2}{m_1+m_2}~v = \frac{m_1-m_2}{m_1+m_2}~v$
$2m_2= m_1-m_2$
$3m_2 = m_1$
$m_2 = \frac{m_1}{3}$
$m_2 = \frac{300~g}{3}$
$m_2 = 100~g$
The mass of the other sphere is $~~100~g$
