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)

A small metal washer is placed on the top of a hemisphere of radius R.

1.	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» Use the condition to FIND minimum velocity , at the top NORMAL reaction = 0 let a velocity v is given in the horizontal direction. now, centripetal FORCE acts then, inward force = outward force mg - N = mv²/R put N = 0 => mg = mv²/R g = v²/R => v² = gR taking square root both sides, v = √gR hence, minimum horizontal SPEED require , v = √gR

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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)

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