In the arrangement shown in the figure, the mass ' m ' will ascend with an acceleration (consider pully and rope are massless) ( g= acceleration due to gravity)

Step-by-step solution

For mass m accelerating upward against gravity, the net force yields T - mg = ma . The heavier mass 3 2 m descends with 3 2 mg - T = 3 2 ma . Adding equations eliminates tension: (T - mg) + ( 3 2 mg - T) = ma + 3 2 ma 1 2 mg = 5 2 ma . Solving for acceleration gives a = 1 2 g 5 2 = g 5 . The acceleration of mass m is g 5 upward .