Is Tension in a Pulley on Triangular Planes Always Equal?

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In the scenario of a pulley at the apex of an isosceles triangle with particles hanging from each side, the tension in the string may not be equal if the masses of the particles differ. The assumption of a non-frictionless pulley implies that it will respond to net torques and rotate, affecting the tension. The mass of the particles is crucial to determining the tension; equal masses would result in equal tension, while differing masses would lead to unequal tension. Clarification on the mass of the particles is necessary for a complete analysis. Understanding these dynamics is essential for solving the problem accurately.
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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

 
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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.)
 

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