Question

A boy is seated on top of a hemispherical mound of ice of radius R. He is given a little push and he starts sliding down the ice. If ice is frictionless, the boy will leave the ice at a point whose height is

Solution

Correct option is

 

As the boy is given a little push, his initial speed can be taken to be zero. Suppose he leaves the mound at point P at a height h (fig). The forces acting on him are his weight mg and the normal reaction F. It is clear that at point P

                          

Where v is the speed of the boy at P. This is the speed with which he leaves the ice. Energy conservation gives   

                          

Using Eq. (i) and (ii) we get,  

                          

As the boy leaves the mound, the normal reaction F vanishes. Thus, putting F = 0 in Eq. (iii), we have

                          

 Therefore, we get

                  

              

 

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