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Question

(A) For a conical pendulum,the time period $T$ is given by $T = 2\pi \sqrt{\frac{h}{g}}$,where $h$ is the vertical height of the pendulum bob from the

Vedclass · Accepted Answer

$\sin 	heta$

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(A) For a conical pendulum,the time period $T$ is given by $T = 2\pi \sqrt{\frac{h}{g}}$,where $h$ is the vertical height of the pendulum bob from the point of suspension.If the string of length $l$ makes an angle $\alpha$ with the vertical,then $h = l \cos \alpha$.In this question,the angle $	heta$ is given with the horizontal. Therefore,the angle with the vertical is $\alpha = 90^\circ - 	heta$.Substituting this into the expression for height: $h = l \cos(90^\circ - 	heta) = l \sin 	heta$.Thus,the time period is $T = 2\pi \sqrt{\frac{l \sin 	heta}{g}}$.Squaring both sides,we get $T^2 = 4\pi^2 \frac{l \sin 	heta}{g}$.Since $4\pi^2$,$l$,and $g$ are constants,we have $T^2 \propto \sin 	heta$.

If the string of a conical pendulum makes an angle $\theta$ with the horizontal,then the square of its time period is proportional to

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