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 ?

Question

Infinity Learn · Accepted Answer

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=23$$θ$$=$$$$sin$$−$$1$$⁡$$23=42$$∘

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 ?

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