Question

A stone of mass ‘m’ at the end of a string of length ‘l’ is whirled in a vertical position at a constant speed. The tension in the string will be minimum when the stone is at the

• A. Bottom of the circle
• B. Half-down from the top
• C. Quarter way down from the top
• D. Top of the circle

Hint:

In vertical circular motion, the tension is minimum at the top because gravity assists the centripetal requirement.

Answer 1

The Correct Option is D

In vertical circular motion, the tension in the string varies with the position of the mass due to the effect of gravity.
At the top of the circle, both the weight of the stone (\( mg \)) and the centripetal force (\( \frac{mv^2}{l} \)) act in the same direction (toward the center).
The tension \( T \) in the string at the top is given by: \[ T_{top} = \frac{mv^2}{l} - mg \] At the bottom of the circle, the tension must overcome gravity and provide the centripetal force: \[ T_{bottom} = \frac{mv^2}{l} + mg \] Therefore, tension is minimum at the top of the circle and maximum at the bottom.