A mass of 2 kg is whirled in a circle in a horizontal plane, at an initial speed of 5 revolutions per min. Keeping the radius constant, the speed is increased, so that the centripetal force is four times the initial value. The ratio of the final speed to initial speed is ------

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Solution

Dear student, Given : mass=2kg Initial speed=Ï‰=5rpm=5x2Ï€/60 rad/sec =Ï€/6 rad/sec Tension=Centripetal force= mrÏ‰² T=2xrx(Ï€/6)² T =mrÏ‰²=2xrxÏ€²/36--------- 1 If centripetal force is made four times, then tension also will be four times of initial . 4T=mrÏ‰â‚²=4x[2xrxÏ€²/36] ----- 2 where Ï‰â‚² is the new angular speed Dividing equation 2 by 1 we get Ï‰â‚²=4Ï‰² Ï‰â‚=2Ï‰=2x5=10rpm âˆ´New angular speed will be 2 times initial angular speed. So ratio will be 2:1. Regards

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