Question

Part a consider another special case in which the inclined plane is vertical (θ=π/2). in this case, for what value of m1 would the acceleration of the two blocks be equal to zero?

Answer 1

The answer would be m1 = m2

FBD of m1 is the sum of the forces in the y direction = 0 
0 = T - m1*g 
transposing:
m1*g = T 

FBD of m2 is the sum of the forces in the y direction = 0 
0 = T - m2*g 
transposing:
m2*g = T 

set them equal to each other and solve for m1 
m1*g = m2*g

= m1 = m2

 

Explanation:

The force on individual mass would be downwards or descending and equal to the tension shaped by the other mass, which would be upward or rising by the act of the seamless pulley, so the forces cancel on each mass.