A rope can withstand a tension of 3 N. If an object weighing 200 grams is attached to the rope of length 1 m and revolved, at what angular velocity will the rope snap?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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An object is attached to a rope and rotated. The mass of the object is 200 g. The rope can withstand a maximum tension of 3 N after which it would snap.

When the object is rotated there is a centrifugal force created that pushes the object outwards. The force by which it is pushed outward is given by m*v^2/r. Here we are given m = 200 g, r = 1 m and v has to be determined. As the maximum tension that the string can withstand is 3 N, we equate that to the centrifugal force and solve for the velocity v.

3 = 0.2*v^2/1

=> v = sqrt(3/0.2) = sqrt(15)

The corresponding angular velocity is given by v/r = sqrt(15) = 3.87 rad /s

The angular vellocity beyond which the rope snaps is 3.87 rad/s.