# A small disc is on top of a hemisphere of radius R. What is the smallest horizontal velocity v that should be given to the disc for it to leave the hemisphere and not slide down ? (assume there is no friction)

$(a)\;v=\sqrt {2gR}\quad (b)\;v=\sqrt {gR} \quad (c)\;v=\sqrt {2R} \quad (d)\;v=\sqrt {g^2 R}$

At the top the normal reaction should be zero
When a velocity v is given in the horizontal direction Centripetal force acts
Therefore $mg-N=\large\frac{mv^2}{R}$
When N=0
$v=\sqrt {gR}$