Question

A stone is rotated along a circle in a horizontal plane by means of a horizontal string at some height above the ground. If the string cut, the stone moves along:
A) A radial straight line.
B) A tangential straight line.
C) A parabolic path in a horizontal plane.
D) A parabolic path in a vertical plane.

Answer 1

Here we have given a stone which is rotating in a circular motion in a horizontal plane which is attached to a horizontal string. We have to find the motion of stone if the string is cut. So we can draw a simple diagram and using some basic laws which are applied on objects in circular motion we can find the path stone will take when the string is cut.

Complete step by step answer:
Let us draw a diagram for the above question.

Here O is the center of the circle in which the stone S attached to the string is moving at some height h above the ground. As the stone is moving in a circular motion, the direction of velocity will be changing and it will be always tangential to the plane of the motion. Here it will be tangential to the horizontal plane and in the above diagram its direction is shown where v is the velocity of the stone and the arrow shows the direction of velocity.
So when the string is cut it will move in the direction of its velocity which is tangential but as it is situated at height h from ground it experiences downward pull and so it will follow a parabolic path with the horizontal plane.

So, the correct answer is “Option C”.

Note: Here while the object is in motion also it has some gravitational pull which is balanced by the tension in the string but once it is cut it is unbalanced and it falls toward ground. The stone does not fall down vertically because of the direction of velocity i.e. it will move tangentially straight but falls down gradually and so follows a parabolic path. One can therefore mistakenly assume option B is correct.