Q. 35.0( 5 Votes )

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 :

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


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