Question

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. If, the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks -

• A. the stone moves radially outwards
• B. the stone flies off tangentially from the instant the string breaks
• C. the stone flies off at an angle with the tangent whose magnitude depends on the speed of the particle ?

Answer 1

The Correct Option is B

To solve this problem, we need to understand what happens when an object moves in a circular path and suddenly loses the centripetal force that keeps it moving in that path.

1. **Concept of Circular Motion:** - When an object is tied to a string and whirled around in a circle, it moves in circular motion. The string applies a centripetal force directed towards the center of the circle, maintaining the object's curved path.

2. **Effect of String Breaking:** - The centripetal force is the only force keeping the stone in its curved path. If the string breaks, there is no longer any force acting towards the center of the circle.

3. **Newton's First Law of Motion:** - According to Newton's first law, an object in motion will continue in its current state of motion unless acted upon by an external force. At the instant the string breaks, there is no centripetal force, and no other force acts on the stone. - Therefore, the stone will continue moving in the path it was taking at the instant the string breaks, which is tangential to the circle.

4. **Conclusion:** - Since the stone will move in the same direction it was heading at the moment of the break, it flies off tangentially to the circle.

Thus, the correct option is: the stone flies off tangentially from the instant the string breaks.