Figure-shows-a-small-bob-of-mass-m-suspended-from-a-point-on-a-thin-rod-by-a-light-inextensible-string-of-length-l-The-rod-is-rigidly-fixed-on-a-circular-platform-The-platform-is-set-into-rotation-

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Question Number 21131 by Tinkutara last updated on 13/Sep/17

$$\mathrm{Figure}\mathrm{shows}\mathrm{a}\mathrm{small}\mathrm{bob}\mathrm{of}\mathrm{mass}m$$$$\mathrm{suspended}\mathrm{from}\mathrm{a}\mathrm{point}\mathrm{on}\mathrm{a}\mathrm{thin}\mathrm{rod}$$$$\mathrm{by}\mathrm{a}\mathrm{light}\mathrm{inextensible}\mathrm{string}\mathrm{of}\mathrm{length}$$$$l.\mathrm{The}\mathrm{rod}\mathrm{is}\mathrm{rigidly}\mathrm{fixed}\mathrm{on}\mathrm{a}\mathrm{circular}$$$$\mathrm{platform}.\mathrm{The}\mathrm{platform}\mathrm{is}\mathrm{set}\mathrm{into}$$$$\mathrm{rotation}.\mathrm{The}\mathrm{minimum}\mathrm{angular}\mathrm{speed}$$$$\omega ,\mathrm{for}\mathrm{which}\mathrm{the}\mathrm{bob}\mathrm{loses}\mathrm{contact}\mathrm{with}$$$$\mathrm{the}\mathrm{vertical}\mathrm{rod},\mathrm{is}$$$$\left(1\right)\sqrt{\frac{g}{l}}$$$$\left(2\right)\sqrt{\frac{2g}{l}}$$$$\left(3\right)\sqrt{\frac{g}{2l}}$$$$\left(4\right)\sqrt{\frac{g}{4l}}$$

Commented by ajfour last updated on 13/Sep/17

$$\sin \theta \approx \theta =\frac{r}{l}$$$$T\cos \theta \approx T=mg$$$$T\sin \theta \approx T\theta =T\left(\frac{r}{l}\right)=m{\omega }^{2}r$$$$\Rightarrow mg\left(\frac{r}{l}\right)=m{\omega }^{2}r$$$$or\omega =\sqrt{\frac{g}{l}}.option\left(1\right).$$

Commented by ajfour last updated on 13/Sep/17

Commented by Tinkutara last updated on 13/Sep/17

Commented by Tinkutara last updated on 13/Sep/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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