Question

A stone of mass \( m \), tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is:

• A. the same throughout the motion
• B. minimum at the highest position of the circular path
• C. minimum at the lowest position of the circular path
• D. minimum when the rope is in the horizontal position

Hint:

The tension in the string is minimum at the highest point because gravity assists in providing the centripetal force at that position.

Answer 1

The Correct Option is B

Step 1: The tension in the string depends on both the centripetal force and the gravitational force acting on the stone. At the highest position, the stone is moving upwards, and gravity opposes the tension in the string. 
Step 2: The tension in the string is given by the equation: \[ T = \frac{mv^2}{r} - mg. \] At the highest position, the tension is the smallest because the gravitational force acts in the same direction as the centripetal force. 
Step 3: Hence, the tension in the string is minimum at the highest point of the circular path.