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A stone of mass m tied to a string of le...

A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will move

A

towards the centre

B

away from the centre

C

along a tangent

D

will stop.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the motion of the stone when the string breaks. Here's a step-by-step breakdown of the solution: ### Step 1: Understand the Circular Motion The stone is tied to a string and is rotating in a circular path with a constant speed \( v \). The tension in the string provides the necessary centripetal force to keep the stone moving in a circle. **Hint:** Remember that in circular motion, the object is constantly changing direction, which requires a centripetal force directed towards the center of the circle. ### Step 2: Identify the Forces Acting on the Stone While the stone is in circular motion, the tension in the string acts as the centripetal force. If the string breaks, the tension force will no longer act on the stone. **Hint:** Consider what happens to the forces acting on the stone when the string is cut. ### Step 3: Analyze the Instant the String Breaks At the moment the string breaks, the stone has a velocity \( v \) directed tangentially to the circular path. Since there is no longer any tension acting on the stone, there is no net force acting on it to change its state of motion. **Hint:** Recall Newton's first law of motion, which states that an object in motion will remain in motion with the same speed and in the same direction unless acted upon by a net external force. ### Step 4: Determine the Path of the Stone After the String Breaks When the string breaks, the stone will continue to move in the direction it was moving at that instant, which is along the tangent to the circular path. Therefore, it will move away from the center of the circle in a straight line. **Hint:** Visualize the motion: if you were to draw a tangent to the circle at the point where the stone was located when the string broke, that would be the direction the stone travels. ### Conclusion The correct answer is that if the string breaks, the stone will move along the tangent to the circle at the point of breakage. **Final Answer:** The stone will move along the tangent (Option C).
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