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A stone tied to a string of length l is ...

A stone tied to a string of length `l` is whirled in a horizontal circle at a constant angular speed `omega` in a circle of radius r. If the string makes an angle `theta` with vertical then the tension in the string is :

A

`m(g cos theta+omega^ (2)r)`

B

`msqrt(omega^(4)r^(2)+g^(2))`

C

`msqrt(omega^(2)r^(2)+g^(2))`

D

`m(g cos theta -omega^(2)r)`

Text Solution

AI Generated Solution

The correct Answer is:
To find the tension in the string when a stone is whirled in a horizontal circle at a constant angular speed, we can follow these steps: ### Step 1: Understand the forces acting on the stone The stone experiences two main forces: 1. The gravitational force acting downwards, which is \( mg \). 2. The tension \( T \) in the string, which has two components: - A vertical component \( T \cos \theta \) that balances the weight of the stone. - A horizontal component \( T \sin \theta \) that provides the centripetal force required for circular motion.
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