Gravity exerts a normal force on the dome of
forcenormal=mg*CosTheta where theta is measured from the vertical to the point of contact.
c. when mv^2/r>normal force, it takes off.
now v is the result of gravity PE converting to KE.
let Theta=90 deg=zero PE point, or referece.
then at the top, PE=mgr
PE at any other point then is
PE(Theta)=mgr*cosTheta
so KE= mgr(1-cosTheta)
or 1/2 m v^2=mgr (1-cosTheta)
v^2 = 2gr (1-cosTheta)
finally, when mv^2/r >mgcosTheta
2g ((1-cosTheta)> gcosTheta
1/2 -1/2 cosTheta>cosTheta
or -3/2 cosTheta>-1/2
or cosTheta<1/3 and at the angle
Theta=arccos 1/3= 70.58 degrees it flys off.
check my thinking and my work.