Physics - W.E.P. Question with Solution | TestHub
A point like object of mass is able to move up and down on a vertical fixed rod. There is a vertical hole at the centre of the object, and the rod fits into this hole, such that the object can slide along the rod frictionlessly. Two pieces of thin light threads are attached to the object, and initially the angle between both threads and the vertical is . Each thread goes through a pulley, which are at the same height, and at the other end of each thread an object of mass kg is tied. The system is released from rest. After releasing the system it stops at the position where the threads attached to it are horizontal.
Options:(select one or more)
Answer:
Solution:
Let be the distance the object rises and the distance each mass descends when the system stops with both threads horizontal.
Applying the work--energy theorem from the initial to the final state (i to f),
Keeping the length of each string constant (the slant thread shortens from to as rises to the pulley level, since the initial angle is ), From (i) and (ii),
so (A) is correct. In the final state the threads are horizontal, so the tension in each thread has no vertical component on ; the only vertical force on is , and its instantaneous acceleration as it starts to move back has to be . Hence (C) is correct and (B) is false. At the same moment the acceleration of along each (horizontal) thread is zero, so the acceleration of each mass is zero, not ; (D) is false.
