IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Lift a Weight by Moving another Weight in a Circle

## Objective

To study centripetal force in rotational motion.

## Apparatus

plastic body of a pen, thread, two different masses.

## Procedure

Pass a thread through the both side open plastic body of a used pen. Tie two unequal masses $$m$$ and $$M$$ on the two sides of the thread. Hold the plastic body in vertical position in your hand with the heavier mass $$M$$ hanging and the lighter mass $$m$$ resting at the top of the plastic body. Give motion to the masses by rotating your hand little bit so that the upper mass is set in nearly circular motion. As soon as it acquires sufficient speed it will pull the hanging body up. If you speed up the rotating body the heavier hanging mass can move right up to the plastic body.

You can adjust the speed of the rotating body by manipulating the force provided by your hand. By properly adjusting this force, you can keep the hanging body fixed at a desired height.

## Discussion

This phenomenon can be explained in a number of ways. The tension in the thread, which provides the centripetal force, should be $$mv^2/r$$. But this tension should also be equal to $$Mg$$, the weight of the hanging body if it remains in equilibrium. Thus $$mv^2/r = Mg$$. Now when you increase the speed of the rotating mass $$m$$ by adjusting the force from your hand, the tension $$mv^2/r$$ is increased and hence the mass $$M$$ moves up with acceleration.

You can also show conservation of angular momentum, $$L=mwr^2$$, by demonstrating increase of $$\omega$$ when $$r$$ is reduced (by pulling the thread).