Answer
(a) stay the same
(b) by a factor of 2.
Work Step by Step
(a) We know that the acceleration of the system is given as
$a=(\frac{m_2}{m_1+m_2})g$
But given that $m_1=2m_1$and $m_2=2m_2$
$\implies a_{new}=(\frac{2m_2}{2m_1+2m_2})g$
$\implies a_{new}=\frac{2}{2}(\frac{m_2}{m_1+m_2})g$
$\implies a_{new}=a$
Thus, the acceleration will stay the same.
(b) We know that the tension is given as
$T=(\frac{m_1m_2}{m_1+m_2})g$
But $m_1=2m_1$ and $m_2=2m_2$
$\implies T_{new}=(\frac{(2m_1)(2m_2)}{2m_1+2m_2})g$
$\implies T_{new}=\frac{4}{2}(\frac{m_1m_2}{m_1+m_2})g$
$\implies T_{new}=2T$
Thus, the tension in the string is increased by a factor of 2.