Is Tension in a Pulley on Triangular Planes Always Equal?

[fickle]

Homework Statement

There's a pulley at the apex of an isosceles triangle, with a particle hanging from the string at each side (plane). Would the tension in this string be the same in this situation?

Homework Equations

The Attempt at a Solution

 

[dynamicsolo]

I'm assuming in this problem that the pulley is not frictionless, so it will respond to net torques and rotate. Are the "particles" on each side of the pulley equal in mass, or different? (It matters in this situation.)