a$)(20$ p$)$ A boy is seated on the top of a hemispherical mound of ice, of radius $R,$ shown in

the figure below. He is given a very small push and starts sliding down the ice. Show that

he leaves the ice at a point $2\frac{R}{3}($as measured from the centre of the hemisphere$),$ if the ice

is practically frictionless. For the purpose in question, you are supposed to write that at the

point the boy leaves the ice, the radial component of his weight, is balanced by the

centrifugal force he is experiencing, due to the rotational motion. Use further the energy

conservation law.

b$)(5$ p$)$ What is his velocity at the point the boy leaves the ice, if $R=2m?($Take $g=10$

$\frac{m}{s^2}.)$

c$)(5$ p$)$ How would you alter your approach, if you had to take into account the friction?

Explain in a few words.