Question

In the case of conical pendulum, if \( T \) is the tension in the string and \( \theta \) is the semi-vertical angle of the cone, then the component of tension which balances the centrifugal force in equilibrium position is

• A. \( T \sin \theta \)
• B. \( \frac{T \sin \theta}{2} \)
• C. \( T \tan \theta \)
• D. \( T \cos \theta \)

Hint:

In conical pendulum problems, the component of the tension that balances the centrifugal force is always the horizontal component, \( T \sin \theta \).

Answer 1

The Correct Option is A

Step 1: Understanding the forces.
In a conical pendulum, the forces acting on the bob are the tension \( T \) and the centrifugal force. The tension is resolved into two components: one along the string (\( T \cos \theta \)) and one perpendicular to the string (\( T \sin \theta \)). The centrifugal force is balanced by the horizontal component of the tension.
Step 2: Conclusion.
Thus, the component of the tension that balances the centrifugal force is \( T \sin \theta \), which corresponds to option (A).