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Question

A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle 30 to the power of ring operator end exponent with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration 'a'. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be N subscript A B end subscript text  and  end text N subscript B C end subscriptrespectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a ' of the carriage is increased, pick up the correct statement:

  1. N subscript A B end subscript increases and N subscript B C end subscript decreases    
  2. Both N subscript A B end subscript and N subscript B C end subscript increase    
  3. N subscript A B end subscript remains constant and N subscript B C end subscript increases    
  4. N subscript A B end subscript increases and N subscript B C end subscriptremains constant    

The correct answer is: N subscript A B end subscript remains constant and N subscript B C end subscript increases


    The free body diagram of cylinder is as shown. Since net acceleration of cylinder is horizontal

    N subscript A B end subscript cos invisible function application 30 to the power of ring operator end exponent equals m g text  or  end text N subscript A B end subscript equals fraction numerator 2 over denominator square root of 3 end fraction m g
    and NBC – NAB sin30° = ma or NBC = ma + NAB sin 30° .... (2)
    Hence NAB remains constant and NBC increases with increase in a.

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