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  4. A sphere of mass 0.20 kg is attached to an inextensible string of length 0.5m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be

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Q. A sphere of mass 0.20 kg is attached to an inextensible string of length 0.5m whose upper end is fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 0.3 m. The speed of the sphere will be

JamiaJamia 2010

Solution:

As shown in figure
$ T\sin \theta =\frac{m{{v}^{2}}}{r} $ $ T\cos \theta =mg $ So, $ \tan \theta =\frac{{{v}^{2}}}{rg}=\frac{r}{\sqrt{{{l}^{2}}-{{r}^{2}}}} $ $ \therefore $ $ v={{\left[ \frac{{{r}^{2}}g}{{{({{l}^{2}}-{{r}^{2}})}^{1/2}}} \right]}^{1/2}} $ $ ={{\left[ \frac{0.09\times 10}{{{(0.25-0.09)}^{1/2}}} \right]}^{1/2}}=1.5\,m/s $

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