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A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes:
T = m ω² r -> T ∝ ω² -> When ω is doubled (2ω), tension quadruples: (2)² = 4T!
For a mass m whirled in a horizontal plane of radius r on a frictionless surface, the tension T in the string provides the necessary centripetal force directed toward the center of the circle:
When the speed is increased to ω_new = 2ω while keeping the radius r unchanged, the new tension T_new becomes:
Expanding the squared term:
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Inverts the relationship (would occur if speed were halved).
Incorrect exponent; occurs if T ∝ √ω was used.
Ignores speed increase.
Direct consequence of T ∝ ω²: (2)² = 4.
Students in a rush sometimes write T ∝ ω and pick 2T (though 2T was not among the options here, keeping it foolproof).
"Centripetal force is directly proportional to the square of angular velocity (F_c = m ω² r)."
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