Question

A small block slides down from the top of hemisphere of radius R. At what height (h) the block will lose contact with the surface of the sphere assuming there is no friction between the block and hemisphere.

Answer 1

Let the body loses the contact of the sphere when it is at point A whose height is h. It means the block has fallen through height (R - h).

Now v² - u² = 2gx

or, v² - 0 = 2g (R - h)

or, v² = 2g (R - h)

Now, centripetal acceleration at A

= v²/R = 2g(R - h)/R .....(i)

The component of 'g' along AO

= g cosθ .....(ii)

The body loses contact, it