Question

A stone of mass 2 kg is fastened to one end of a steel wire of cross sectional area 2 mm and is
whirled in a horizontal circle of radius 25cm. If the breaking stress of steel is 1.2x10°Nm 2 find the
maximum number of revolutions the stone can make per minute without the string breaking.​

Answer 1

Explanation:

Given A stone of mass 2 kg is fastened to one end of a steel wire of cross sectional area 2 mm and is  whirled in a horizontal circle of radius 25cm. If the breaking stress of steel is 1.2 x 10^9 Nm ^-2 find the  maximum number of revolutions the stone can make per minute without the string breaking.

Given mass of stone m = 2 kg

Steel wire of cross sectional area A = 2 mm^2 = 2 x 10^-6 m^2

Breaking stress of steel is y = 1.2 x 10^9 Nm^-2

Radius r = 25 cm = 0.25 m

Tension T = mrω^2  

So Y = T / A

         = mrω^2 / A

    So ω = √YA / mr

            = √1.2 x 10^9 x 2 x 10^-6 / 2 x 0.25

            = 69.28 rad/s

Now ω = 2 π f / 60

So f = 60 ω / 2π

      = 60 x 69.28 / 2 π

So f = 661.57 rev / min

Now without breaking the string the maximum number of stone can make per minute is 661.57 rev / min

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