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JEE MainPhysicsMotion in Two Dimensions

Two stones, A and B, are being whirled in horizontal circles by two different strings. The ratio of the mass of stone A to the mass of stone B is 2:1 , and the ratio of the lengths of their respective strings is 1:2 . If the ratio of the maximum breaking tensions of the strings is 4:1 , what is the ratio of the maximum angular speeds ( _A : _B ) with which the stones can be whirled?

Options

  1. A1:2
  2. B4:1
  3. C1:4
  4. D2:1

Correct answer

D. 2:1

Step-by-step solution

The maximum tension T in the string provides the necessary centripetal force for circular motion: T = m ^2 r Rearranging for angular speed : = T mr The ratio of the maximum angular speeds of the two stones is: _A _B = T_A T_B m_B m_A r_B r_A Substitute the given ratios m_A m_B = 2 1 , r_A r_B = 1 2 , and T_A T_B = 4 1 : _A _B = ( 4 1 ) ( 1 2 ) ( 2 1 ) = 4 = 2 Thus, the ratio _A : _B is 2:1 . Answer: 2:1

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