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(A) For a conical pendulum,the bob moves in a horizontal circle of radius $r = l \sin 	heta$,where $l$ is the length of the string and $	heta$ is th

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(A) For a conical pendulum,the bob moves in a horizontal circle of radius $r = l \sin 	heta$,where $l$ is the length of the string and $	heta$ is the angle with the vertical.The forces acting on the bob are tension $T$ along the string and weight $mg$ downwards.The vertical component of tension balances the weight: $T \cos 	heta = mg \implies T = \frac{mg}{\cos 	heta}$.The horizontal component provides the centripetal force: $T \sin 	heta = m \omega^2 r = m \omega^2 (l \sin 	heta)$.From the horizontal component,$T = ml \omega^2$. This implies that for a fixed length $l$,$T$ is directly proportional to $\omega^2$.However,as $\omega$ increases,the angle $	heta$ increases. At $\omega = 0$,the bob is at rest,and $T = mg$. As $\omega$ increases,the bob starts moving in a circle,and the tension increases as $T = ml \omega^2$ (for small angles,$T \approx mg + \frac{1}{2}ml\omega^2$ is a common approximation,but generally $T$ increases with $\omega^2$).Looking at the options,option $A$ represents the behavior where $T$ starts at $mg$ (at $\omega=0$) and increases with $\omega^2$ as the pendulum gains angular velocity.

In a conical pendulum,the bob is rotated with different angular velocities and the tension in the string is calculated for different values of $\omega$. Which of the following is the correct graph between $T$ and $\omega$?

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