A small block is placed at the top of a sphere. It slides on the smooth surface of the sphere. What will be the angle made by the radius vector of the block with the horizontal when it leaves the surface ?

Here      mv2R=mgsin⁡θ                     ...(1)The speed is acquired by the block after falling through a distance h. Hence12mv2=mgh  or  v=2gh       …(2)∴ m(2gh)R=mgsin⁡θ=mg(R−h)Ror      2h=R−h  or  h=R/3From figure,sin⁡θ=R−hR=R−R/3R=23θ=sin−1⁡23=42∘