Find the acceleration of two masses as shown in figure . The pulley are light and frictionless and string are light and frictionless and string are light and inextensible.

Explanation

Writing equations of motion

For `M 5 T - Mg = ma_(1)` …(i)
For `m Mg - T = ma_(2)` …(ii)
from constrain equation,
`a_(2) = 5a_(1)` …(iii)
Solving these equation, we get acceleration of `M`
`a_(1) = ((5m - M)/(25m + M)) g`
and of `m, a_(2) = 5 ((5m - M)/(25m + M)) g`