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As shown in the figure, wheel A of radius r A = 10 c m is coupled by a belt B to the wheel C of radius r C = 25 c m . The angular speed of wheel A is increased from rest at a constant rate of 1.6 r a d s - 2 . Time after which wheel C reaches a rotational speed of 100 r p m , assuming the belt does not slip, is nearly

Options

  1. A4 s
  2. B8 s
  3. C12 s
  4. D16 s

Correct answer

D. 16 s

Step-by-step solution

a t = α A   r A = α C r C α C =   α A   r A r C =   1.6 × 10 25 = 0.64   rad   s - 2 t = ω C α C = 100 × 2 π 60 0 .64 = 16.35  s

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