Please excuse the crude drawings
The question is, if I burn the thread t, how will the reading in the spring balance(S) change? Ie, increase, decrease, or remain the same?
When we burn the thread, the objects will move, but the tension should increase a bit. ( I can't explain this, I only get this intuitively.) and, since the spring balance reads the double of the tension, I think this should make it a lot more than the initial reading. Since if the tension in the intact string changes by $\triangle T$, the reading should increase by $2 \triangle T$. That's all I can think of. So as you see, my approach is very intuitive, and hence I am asking this in order to get a logical and stronger reasoning