Question

in an experiment a rubber stopper is attached to one end of a string that is passed through a plastic tuber before weights are attached to the other end. the stopper is whirled in an horizontal circular path at a constant speed. What would happen to the radius of the circle if the student whirls the stopper at a greater speed without changing the weights.

Answer 1

As we know that weight is attached at the other end of the string and that weight remains constant.

So here we can say that tension in the string will always remain same

$T = mg$

now for the stopper on the other side is revolving in horizontal circle with some speed. for this circular motion the Tension force will provide centripetal force to it.

So here for the stopper we can say

$T = \frac{Mv^2}{R}$

now since tension always remains same as the suspended mass is fixed so if we increase the speed of the stopper the radius must have to increase so that tension will be same in the string