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Two cyclists A and B are moving with uniform circular motion on identical circular tracks. Cyclist A completes one revolution in 3 minutes, while cyclist B completes one revolution in 4 minutes. What is the ratio of the angular distances covered by A and B ( _A : _B ) in a time interval of 12 minutes?

Options

  1. A4 : 3
  2. B3 : 4
  3. C1 : 1
  4. D16 : 9

Correct answer

A. 4 : 3

Step-by-step solution

The angular distance covered by a particle in uniform circular motion is given by = t = ( 2 T )t . For cyclist A, the time period T_A = 3 minutes . For cyclist B, the time period T_B = 4 minutes . Since the time interval t = 12 minutes is the same for both cyclists, the ratio of their angular distances is inversely proportional to their time periods: _A _B = T_B T_A _A _B = 4 3 Thus, the ratio is 4 : 3 . Answer: 4 : 3

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