[Rehaan_genius]

this question is from the topic "center of mass"
question is very simple, you just need to answer whether the right block will hit the pulley first or the left block will hit the wall first if the system is released from rest(all the surfaces are frictionless).
It's a tricky question, no need to calculate and no need to apply any equation, just answer with a complete logic/reason.
Let see, who can solve this!!

[Capuchin]

It looks to me like the system will just sit at rest. Am I missing something?

[ebaines]

I think the question is asked wrong - it looks to me that when the right block is released it will fall and swing int the wall, whereas the left block will side toward the right and ultimately hit the pulley. Right?

I'll take a shot at it. If you think about the tension T in the rope, at every instant it has the same value at both the left and right blocks. At the right block, T can be resolved into horizontal and vertical components. Note that the horizontal component is always less than T (except for the brief instant when the angle theta is 0). So the horizontal force acting to move the right block towards the left is always less than the horizontal force acting to move the left block toward the right. Hence the left block moves horizontally faster than the right block moves horizontally. Conclusion: the left block meets the pulley before the right block meets the wall.

Here's another way to look at it: the only horizontal force applied externally to the two-mass system is from the pulley - it exerts a force upwards and to the right, at angle theta. Consequently it exerts a horizontal force to the two mass system, and so the center-of-mass of the two bock system moves to the right.

[Capuchin]

Oh it's a rope? I assumed it were a rod! Since we are not told either way I will assume it is a rod and say the answer is "neither"!

[Rehaan_genius]

OHH!! I missed one thing! When the system is released from rest the string will remain streched all the time.

[Rehaan_genius]

And guys, the question is absolutely right!

[Rehaan_genius]

Ebaines is right! Well done! I appreciate!

[Rehaan_genius]

Yes one more mistake! Interchange Left-right in the question!(sorry guys)

[asking]

I looked at it without looking at the answers and concluded the right block would hit the wall and THEN drag the other block into the pulley as the right block fell/slid downward.. Hope that's right!