c
(c)
$\left(m_1+m_2\right) a_{\text {max }}=f$
$\rightarrow F=\mu N$
$N=m_1 g$
$m_2 a_{\text {max }}=\mu m_1 g$
$a_{\text {max }}=\mu \frac{m_1}{m_2} g$
$F=\left(m_1+m_2\right) \mu \frac{m_1}{m_2} g$
$= m_2\left(\frac{m_1}{m_2}+1\right) \mu \frac{m_1}{m_2} g$
$F =\mu m_1\left(\frac{m_1}{m_2}+1\right)$