Neglect friction. Find acceleration of `m, 2 m and 3 m` as shown in the figure. The wedge is find.

Explanation

Writing equation of motion ,
`T - N = 3 ma_(1)` …(i)
` N = 3 ma_(1)` …(ii)
`2 mg - T = 2 ma_(2)` …(iii)
`T - (mg)/(2) = ma_(3)` …(iv)
From constraint equation,
`a_(1) = a_(2) - a_(3)` …(v)
We have five unknown . Solving the above five equatin, we get

`a_(1) = (3)/(17) g`, `a_(2) = (19)/(34) g` and `a_(3) = (13)/(34) g`
Acceleration of `m = a_(3) = (13)/(34) g`
Acceleration of `2 m = sqrt (a_(1)^(2) + a_(2)^(2)) = (sqrt 397)/(34) g`
and acceleration of `3 m = a_(1) = (3)/(17) g`