Problem $4(30$ points$)$

In the figure, block $1$ has mass $m_1=480g,$ block $2$ has mass $m_2=510g,$ and the pulley is on a frictionless horizontal axle $($pulley can be viewed as a disc$)$ and has radius $R=4\mathrm{.}6cm.$ When released from rest, block $2$ falls $80cm$ in $6s$ without the cord slipping on the pulley.

$($a$)(10$ points$)$ What is the magnitude of the acceleration of the blocks?

$($b$)(10$ points$)$ What is the tension $T_2($the tension force on the block $2$

$($c$)(10$ points$)$ What is the tension $T_1($the tension force on the block $1($Use $g=10\frac{m}{s^2})$