A heavy, big sphere is hung from a string of length $\ell$. The sphere moves in a horizontal circular path making an angle $ heta$ with the vertical. Its time period is:

Question

A heavy, big sphere is hung from a string of length $\ell$. The sphere moves in a horizontal circular path making an angle $	heta$ with the vertical. Its time period is:

Accepted Answer

$T=2\pi\sqrt{\frac{\ell\cos	heta}{g}}$. This is a conical pendulum. From vertical balance, $T\cos	heta=mg$, and from horizontal centripetal force, $T\sin	heta=m\omega^2 r$ with $r=\ell\sin	heta$. Combining these gives $\omega^2=g/(\ell\cos	heta)$, so the time period is $2\pi\sqrt{\ell\cos	heta/g}$.

A heavy, big sphere is hung from a string of length $\ell$. The sphere moves in a horizontal circular path making an angle $\theta$ with the vertical. Its time period is:

Solution

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