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Q.

A ball of mass m is attached to the end of a thread fastended to the top of a vertical rod which is fitted to a horizontally revolving round table as shown. If the thread forms an angle $α$ with the vertical, the angular velocity $ω$ of table

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a

$\sqrt{\frac{g}{l \cos α}}$

b

$\sqrt{\frac{r}{g \tan α}}$

c

$\sqrt{\frac{g \tan α}{r + l \sin α}}$

d

$\sqrt{\frac{g \tan α}{r}}$

answer is C.

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Detailed Solution

$T \sin α = m ω^{2} R T \cos α = m g \tan α = \frac{ω^{2} R}{g}$

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$ω = \sqrt{\frac{g \tan α}{R}} = \sqrt{\frac{g \tan α}{r + l \sin α}}$

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A ball of mass m is attached to the end of a thread fastended to the top of a vertical rod which is fitted to a horizontally revolving round table as shown. If the thread forms an angle α with the vertical, the angular velocity ω of table