A rubber stopper on the end of a string is swung steadily on a horizontal fricti

Question

A rubber stopper on the end of a string is swung steadily on a horizontal frictionless table.
In one trial, it moves at speed v in a circle of radius r. In a second trial, it moves at a higher speed 3v in a circle of radius 3r.
(a) In the second trial, its acceleration is
(i) the same as the ?rst trial, (ii) three times larger, (iii) three times smaller, (iv) nine times larger or (v) nine times smaller.
(b) In the second trial, how does its period compare to the ?rst trial. You may use the same choices
as part (a). Explain your answers

Explanation / Answer

a) a = 9v^2/3r = 3 v^2/r (ii) three times larger, period is the same as in first cas e as both time it has the same angular velocity ie.v/r

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