question_answer

A very small particle rests on the top of a hemisphere of radius 20 cm. 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,                                                                 \[\frac{m{{\upsilon }^{2}}}{r}=mg\]                        \[\therefore \]  \[\upsilon =\sqrt{rg}=\sqrt{\frac{20}{100}\times 9.8}=\sqrt{1.96}=1.4\,m/s\]