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AP EAMCET201823 Apr 2018Evening ShiftPhysicsRotational MotionActual

An empty bucket of mass 1 ~kg attached by a light cord passed over a pulley of a water well is released from rest. If the pulley assembly is assumed to be a uniform solid cylinder of mass 8 ~kg and free to rotate about its axis without any friction, then the speed of the bucket as it hits the water 16 ~m below is (take, g=10 ~ms ⁻² )

Options

  1. A4 ~ms ⁻¹
  2. B8 ~ms ⁻¹
  3. C16 ~ms ⁻¹
  4. D20 ~ms ⁻¹

Correct answer

B. 8 ~ms ⁻¹

Step-by-step solution

Torque on pulley =I aligned & m g R= M R^2 2 & = 2 m g M R & aligned So, acceleration of rope, a=R =R 2 m g M R = 2 m g M = 2 1 10 8 = 10 4 ~ms ⁻² Speed of bucket as it falls by 16 ~m is v= 2 a s = 2 10 4 16 = 80 =8.6 8 ~ms ⁻¹

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