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## Homework Statement

A small block slides from rest from the top of a frictionless sphere of radius R.How far below the top,x,does it lose contact with the sphere?(Sphere doesn't move)

## The Attempt at a Solution

The angle subtended by the block at the centre of the sphere can be taken as theta.If the x axis is considered tangential to the surface and hence y axis in the direction of the normal force,this problem can be solved,when combined with the conservation of energy.

N-mg cos(theta)=-mv^2/R

and

mgR(1-cos(theta))=1/2mv^2

N-mg cos(theta)=-mv^2/R

and

mgR(1-cos(theta))=1/2mv^2

Answer is

**R/3.**

My question is,how do you solve this problem if the axes are taken "upright",instead of being inclined.i.e,

**the y-axis is vertical and x-axis is horizontal.**