Answer:[tex]3.79 m/s^2[/tex]
Explanation:
Given
Mass [tex]M=9.5 kg[/tex]
[tex]m=3 kg[/tex]
Net Force is equivalent to [tex]\sum F=ma [/tex]
with tension T in the string
For mass [tex]m[/tex]
[tex]mg-T=ma[/tex]
[tex]T=mg-ma--------1[/tex]
For cylinder
[tex]T\cdot R=I\times \alpha [/tex]
I for solid cylinder is [tex]\frac{2}{5}MR^2 , and \alpha =\frac{a}{R}[/tex]
thus [tex]T=\frac{Ma}{2}----2[/tex]
Substitute the value of T we get
[tex]\frac{Ma}{2}=mg-ma[/tex]
[tex]a(\frac{M}{2}+m)=mg[/tex]
[tex]a=\frac{mg}{\frac{M}{2}+m}[/tex]
[tex]a=3.79 m/s^2[/tex]
