Question

a small block of mass m lies on top of hemisphere of radiys R which is smooth. what minimum horizontal velocity block should be given so that it may not slide down along surface?

Answer 1

Let t-time of falling
v-speed
g-const
then at any period vt=gt^2 /2
it should be>=R

vt=gt^2 /2*& t=2v/g

vt=v*2v/g=2v^2/g>=R

so ans v>=sqrt(0.5gR)