Question

Select and write the most appropriate answer from the given alternatives for each question:
The period of a conical pendulum in terms of its length(I), semivertical angle$\left(\theta \right)$ acceleration due to gravity (g) is

• A. $2\pi \sqrt{\frac{Icos\theta }{g}}$
• B. $\frac{1}{2\pi }\sqrt{\frac{Isin\theta }{g}}$
• C. $\frac{1}{4\pi }\sqrt{\frac{Icos\theta }{4g}}$
• D. $\frac{1}{4\pi }\sqrt{\frac{Itan\theta }{g}}$

Answer 1

The correct option is A $2\pi \sqrt{\frac{Icos\theta }{g}}$

$\begin{array}{c}T\cos \theta =mg\\ T\sin \theta =\left\{\frac{m{v}^2}{r}\right\}\end{array}$

$\begin{array}{c}\cot \theta =\frac{gr}{v^2}\\ \cos \theta =\sqrt{\mathrm{rgtan}\theta }\end{array}$

$\begin{array}{cc}T=\frac{2\pi r}{v}& =\frac{2xr}{\sqrt{rg\tan \theta }}\\ & =2\pi \sqrt{\frac{r}{g\tan \theta }}\\ & =2\pi \sqrt{\frac{\log \theta }{g\tan \theta }}\\ T& =2\pi \sqrt{\frac{l\cos \theta }{g}}\end{array}$