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)

Given;

The radius of hemisphere = R.

The velocity of washer = V.

The centripetal force act on the washer is

F = ………………… (1)

Let the mass of washer is “m”

And acceleration by gravity is “g”

The force by hemisphere on the washer is

F = mg …………. (2)

By Newton’s law of motion every action has an equal reaction but in opposite direction.

∴ Centripetal force on washer = Force by hemisphere on the washer.

From (1) and (2).

= mg;

⇒ v² = gR

⇒ v =

Hence minimum horizontal velocity should be imparted to the washer to detach it from the hemisphere at the initial point of motion is