Question

A small metal washer is placed on the top of a hemisphere of radius R. What minimum horizontal velocity should be imparted to the washer to detach it from the hemisphere at the initial point of motion? (See figure)

Answer 1

use the condition to find minimum velocity ,
at the top normal reaction = 0
let a velocity v is given in the horizontal direction.
now, centripetal force acts
then, inward force = outward force
mg - N = mv²/R
put N = 0 => mg = mv²/R
g = v²/R => v² = gR
taking square root both sides,
v = √gR

hence, minimum horizontal speed require , v = √gR

Answer 2

Answer:

Hope you get this answer as correct