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A very small particle rests on the top of a hemisphere of radius \({20}{c}{m}\). Calculate the smallest horizontal velocity to be given to it if it is to leave the hemisphere without sliding down its surface, take \({g}={9.8}{m}/{s}^{{{2}}}\).
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A very small particle rests on the top of a hemisphere of radius \({20}{c}{m}\). Calculate the smallest horizontal velocity to be given to it if it is to leave the hemisphere without sliding down its surface, take \({g}={9.8}{m}/{s}^{{{2}}}\).

Answer

The particle will leave the hemisphere, when normal reaction \({R}\) becomes zero. In that event,
\(\frac{{{m}\upsilon^{{{2}}}}}{{{r}}}={m}{g}\)
\(\therefore\upsilon=\sqrt{{{r}{g}}}=\sqrt{{\frac{{{20}}}{{{100}}}\times{9.8}}}=\sqrt{{{1.96}}}={1.4}{m}/{s}\)
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