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The iron ball shown is being swung in a vertical circle at theend of a 0.7-m string. How slowly, in m/s, can the ball go throughits top position without

having the string go slack?


At the top position, forces acting on ball are:

force acting downward = weight of ball(mg) and tension
force acting upward = centrifugal force (mv²/r)

given that r = 0.7m
The string will slack just after the tension becomes 0.
So when tension becomes 0, equilibrium equation at top point becomes

mg+T = mv²/r
⇒ mg + 0 = mv²/0.7
⇒ g = v²/0.7
⇒ v² = 0.7g
⇒ v = √0.7g = √(0.7×9.81) = 2.62 m/s

So minimum velocity at the top should be 2.62m/s
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