let tension in left string be T1 and tension in right string be T2.
let the system is moving along the direction of falling of m2.
let acceleration of the system be a .
writing force balance equation for m2:
m2*g-T2=m2*a
==>T2+m*a=m*g
==>T2=m*g-m*a…(1)
writing force balance equation for M:
T2+M*g*sin(theta)-T1=M*a
==>T2-T1-M*a=-M*g*sin(theta)…(2)
writing force balance equation for m1:
T1-m1*g=m1*a
==>T1-m*a=m*g
==>T1=m*a+m*g…(3)
substituting equation 1 and equation 3 in equation 2:
m*g-m*a-(m*g+m*a)-M*a=-M*g*sin(theta)
==>-2*m*a-M*a=-M*g*sin(theta)
==>a=M*g*sin(theta)/(M+2*m)
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